{"id":4459,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/"},"modified":"2019-02-18T16:18:09","modified_gmt":"2019-02-18T10:48:09","slug":"ncert-solutions-class-12-maths-exercise-1-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 1.1"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Relations_and_Functions\" >NCERT Solutions class 12 Maths Relations and Functions<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#Therefore_R_is_neither_reflexive_nor_symmetric_and_nor_transitive\" >Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#Now_is_exactly_7_cm_taller_than_and_is_exactly_7_cm_taller_than_then_it_does_not_imply_that_is_exactly_7_cm_taller_than_R_is_not_transitive\" >Now \u00a0is exactly 7 cm taller than \u00a0and \u00a0is exactly 7 cm taller than \u00a0then it does not \u00a0imply that \u00a0is exactly 7 cm taller than \u00a0R is not transitive.<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#2_Show_that_the_relation_R_in_the_set_R_of_real_numbers_defined_as_R_is_neither_reflexive_nor_symmetric_nor_transitive\" >2. Show that the relation R in the set R of real numbers defined as R = \u00a0is neither reflexive nor symmetric nor transitive.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#3_Check_whether_the_relation_R_defined_in_the_set_1_2_3_4_5_6_as_R_is_reflexive_symmetric_or_transitive\" >3. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = \u00a0is reflexive, symmetric or transitive.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#4_Show_that_the_relation_R_in_R_defined_as_R_is_reflexive_and_transitive_but_not_symmetric\" >4. Show that the relation R in R defined as R = , is reflexive and transitive but not symmetric.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#5_Check_whether_the_relation_R_in_R_defined_by_R_is_reflexive_symmetric_or_transitive\" >5. Check whether the relation R in R defined by R = \u00a0is reflexive, symmetric or transitive.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-2\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#6_Show_that_the_relation_in_the_set_A_1_2_3_given_by_R_1_2_2_1_is_symmetric_but_neither_reflexive_nor_transitive\" >6. Show that the relation in the set A = {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-3\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#7_Show_that_the_relation_R_in_the_set_A_of_all_the_books_in_a_library_of_a_college_given_by_R_is_an_equivalence_relation\" >7. Show that the relation R in the set A of all the books in a library of a college, given by R = \u00a0is an equivalence relation.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-4\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#8_Show_that_the_relation_R_in_the_set_A_1_2_3_4_5_given_by_R_is_an_equivalence_relation_Show_that_all_the_elements_of_1_3_5_are_related_to_each_other_and_all_the_elements_of_2_4_are_related_to_each_other_But_no_element_of_1_3_5_is_related_to_any_element_of_2_4\" >8. Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = \u00a0is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-5\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#9_Show_that_each_of_the_relation_R_in_the_set_A_given_by\" >9. Show that each of the relation R in the set A = \u00a0given by:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-6\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#10_Give_an_example_of_a_relation_which_is\" >10. Give an example of a relation, which is:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-7\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#11_Show_that_the_relation_R_in_the_set_A_of_points_in_a_plane_given_by_R_P_Q_distance_of_the_point_P_from_the_origin_is_same_as_the_distance_of_the_point_Q_from_the_origin_is_an_equivalence_relation_Further_show_that_the_set_of_all_points_related_to_a_point_P_0_0_is_the_circle_passing_through_P_with_origin_as_centre\" >11. Show that the relation R in the set A of points in a plane given by R = {(P. Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P \u00a0(0, 0) is the circle passing through P with origin as centre.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-8\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#12_Show_that_the_relation_R_defined_in_the_set_A_of_all_triangles_as_R_T1_T2_T1_is_similar_to_T2_is_equivalence_relation_Consider_three_right_angle_triangles_T1_with_sides_3_4_5_T2_with_sides_5_12_13_and_T3_with_sides_6_8_10_Which_triangles_among_T1_T2_and_T3_are_related\" >12. Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3 are related?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-9\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#13_Show_that_the_relation_R_defined_in_the_set_A_of_all_polygons_as_R_P1_P2_P1_and_P2_have_same_number_of_sides_is_an_equivalence_relation_What_is_the_set_of_all_elements_in_A_related_to_the_right_angle_triangle_T_with_sides_3_4_and_5\" >13. Show that the relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4, and 5?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-10\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#14_Let_L_be_the_set_of_all_lines_in_XY_plane_and_R_be_the_relation_in_L_defined_as_R_L1_L2_L1_is_parallel_to_L2_Show_that_R_is_an_equivalence_relation_Find_the_set_of_all_lines_related_to_the_line\" >14. Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-11\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#15_Let_R_be_the_relation_in_the_set_1_2_3_4_given_by_R_1_2_2_2_1_1_4_4_1_3_3_3_3_2_Choose_the_correct_answer\" >15. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-12\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#16_Let_R_be_the_relation_in_the_set_N_given_by_R_Choose_the_correct_answer\" >16. Let R be the relation in the set N given by R = \u00a0Choose the correct answer:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#NCERT_Solutions_class_12_Maths_Exercise_11-13\" >NCERT Solutions class 12 Maths Exercise 1.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p><strong>NCERT Solutions class 12 Maths Exercise 1.1<\/strong>\u00a0solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT textbooks. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-relations-and-functions\/1285\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Relations and Functions\u00a0<\/a>as PDF.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20pic.jpg\" alt=\"NCERT Solutions class 12 Maths Exercise 1.1\" width=\"101\" height=\"132\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Relations_and_Functions\"><\/span>NCERT Solutions class 12 Maths Relations and Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong style=\"text-align: justify;\">1. Determine whether each of the following relations are reflexive, symmetric and transitive:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) Relation R in the set A = {1, 2, 3, \u2026\u2026\u2026.. 13, 14} defined as R = <img decoding=\"async\" style=\"height: 27px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image001.png\" \/>.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) Relation R in the set N of natural numbers defined as R =.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = <img decoding=\"async\" style=\"height: 27px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image002.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) Relation R in the set Z of all integers defined as R = <img decoding=\"async\" style=\"height: 27px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image003.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) Relation R in the set A of human beings in a town at a particular time given by:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(a) R = <img decoding=\"async\" style=\"height: 27px; width: 263px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image004.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(b) R = <img decoding=\"async\" style=\"height: 27px; width: 271px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image005.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(c) R = <img decoding=\"async\" style=\"height: 27px; width: 254px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image006.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(d) R = <img decoding=\"async\" style=\"height: 27px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image007.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(e) R = <img decoding=\"async\" style=\"height: 27px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image008.png\" \/><\/strong><\/p>\n<p><strong>Ans. (i)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image009.png\" \/>\u00a0in A = {1, 2, 3, 4, 5, 6, \u2026\u202613, 14}<\/p>\n<p>Clearly R = {(1, 3), (2, 6), (3, 9), (4, 12)}<\/p>\n<p>Since, <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image010.png\" \/>\u00a0R, \u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p>Again <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R but <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image013.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p>Also (1, 3)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R and (3, 9) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R but (1, 9) <img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image015.png\" \/>\u00a0R, \u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<\/p>\n<p>Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/p>\n<p><strong>(ii)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image016.png\" \/>\u00a0in set N of natural numbers.<\/p>\n<p>Clearly R = {(1, 6), (2, 7), (3, 8)}<\/p>\n<p>Now <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image010.png\" \/>\u00a0R, <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p>Again <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R but <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image013.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p>Also (1, 6)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R and (2, 7) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R but (1, 7) <img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image015.png\" \/>\u00a0R, \u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<\/p>\n<h5><span class=\"ez-toc-section\" id=\"Therefore_R_is_neither_reflexive_nor_symmetric_and_nor_transitive\"><\/span>Therefore, R is neither reflexive, nor symmetric and nor transitive.<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p><strong>(iii)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image017.png\" \/>\u00a0in A = {1, 2, 3, 4, 5, 6}<\/p>\n<p>Clearly R = (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (5, 5), (6, 6)<\/p>\n<p>Now <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image018.png\" \/>\u00a0i.e., (1, 1), (2, 2) and (3, 3) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Again <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image019.png\" \/>\u00a0i.e., (1, 2)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R but <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image013.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p>Also (1, 4)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R and (4, 4) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R and (1, 4) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R, <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is reflexive and transitive but not symmetric.<\/p>\n<p><strong>(iv)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image020.png\" \/>\u00a0in set Z of all integers.<\/p>\n<p>Now <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image018.png\" \/>\u00a0i.e., (1, 1) = 1 \u2013 1 = 0 <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0Z\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Again <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image019.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R and\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image021.png\" \/>\u00a0R, i.e., <img decoding=\"async\" style=\"height: 17px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image022.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image023.png\" \/>\u00a0are an integer<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 27px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image024.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0Z and <img decoding=\"async\" style=\"height: 27px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0Z and<\/p>\n<p><img decoding=\"async\" style=\"height: 27px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image026.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R, \u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is reflexive, symmetric and transitive.<\/p>\n<p><strong>(v)<\/strong> Relation R in the set A of human being in a town at a particular time.<\/p>\n<p><strong>(a)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image027.png\" \/><\/p>\n<p>Since <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image028.png\" \/>\u00a0R, because <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0work at the same place. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Now, if <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R and <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R, since <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0work at the same place and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0work at the same place.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Now, if <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R and <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image031.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image033.png\" \/>\u00a0R. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive<\/p>\n<p>Therefore, R is reflexive, symmetric and transitive.<\/p>\n<p><strong>(b)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 267px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image034.png\" \/><\/p>\n<p>Since <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image028.png\" \/>\u00a0R, because <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0live in the same locality. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/><img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image021.png\" \/>\u00a0R because <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0live in same locality and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0also live in same locality. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Again <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>R and <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image031.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/><img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image033.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is reflexive, symmetric and transitive.<\/p>\n<p><strong>(c)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 249px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image035.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is not exactly 7 cm taller than <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>, so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image010.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is exactly 7 cm taller than <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0but <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is not 7 cm taller than <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>, so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R but <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image013.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<h5><span class=\"ez-toc-section\" id=\"Now_is_exactly_7_cm_taller_than_and_is_exactly_7_cm_taller_than_then_it_does_not_imply_that_is_exactly_7_cm_taller_than_R_is_not_transitive\"><\/span>Now <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is exactly 7 cm taller than <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is exactly 7 cm taller than <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image036.png\" \/>\u00a0then it does not \u00a0imply that <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is exactly 7 cm taller than <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image037.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p>Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/p>\n<p><strong>(d)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image038.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is not wife of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>, so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image010.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is wife of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0but <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is not wife of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>, so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R but <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image013.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R and <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image031.png\" \/>\u00a0R then <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image039.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<\/p>\n<p>Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/p>\n<p><strong>(e)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image040.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is not father of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>, so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image010.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is father of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0but <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is not father of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>,<\/p>\n<p>so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R but <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image013.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R and <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image031.png\" \/>\u00a0R then <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image039.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<\/p>\n<p>Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Show_that_the_relation_R_in_the_set_R_of_real_numbers_defined_as_R_is_neither_reflexive_nor_symmetric_nor_transitive\"><\/span><strong>2. Show that the relation R in the set R of real numbers defined as R = <img decoding=\"async\" style=\"height: 29px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image041.png\" \/>\u00a0is neither reflexive nor symmetric nor transitive.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> R = <img decoding=\"async\" style=\"height: 29px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image041.png\" \/>, Relation R is defined as the set of real numbers.<\/p>\n<p><strong>(i) <\/strong>Whether <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image042.png\" \/>\u00a0R, then <img decoding=\"async\" style=\"height: 21px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image043.png\" \/>\u00a0which is false.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p><strong>(ii)<\/strong> Whether <img decoding=\"async\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image044.png\" \/>, then <img decoding=\"async\" style=\"height: 21px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image045.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image046.png\" \/>, it is false. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p><strong>(iii) <\/strong>Now <img decoding=\"async\" style=\"height: 21px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image045.png\" \/>, <img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image047.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image048.png\" \/>, which is false. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive<\/p>\n<p>Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Check_whether_the_relation_R_defined_in_the_set_1_2_3_4_5_6_as_R_is_reflexive_symmetric_or_transitive\"><\/span><strong>3. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = <img decoding=\"async\" style=\"height: 27px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image049.png\" \/>\u00a0is reflexive, symmetric or transitive.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image050.png\" \/>\u00a0R<\/p>\n<p>Now R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)} and <img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image051.png\" \/><\/p>\n<p><strong>(i)<\/strong> When <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image052.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image053.png\" \/>\u00a0which is false, so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image054.png\" \/>\u00a0R, <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p><strong>(ii)<\/strong> Whether <img decoding=\"async\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image044.png\" \/>, then <img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image051.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image055.png\" \/>, false <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p><strong>(iii)<\/strong> Now if <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image056.png\" \/>\u00a0R, <img decoding=\"async\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image057.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image058.png\" \/>\u00a0R<\/p>\n<p><strong>(iv) <\/strong>Then <img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image051.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image060.png\" \/>\u00a0which is false. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<\/p>\n<p>Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Show_that_the_relation_R_in_R_defined_as_R_is_reflexive_and_transitive_but_not_symmetric\"><\/span><strong>4. Show that the relation R in R defined as R = <img decoding=\"async\" style=\"height: 27px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image061.png\" \/>, is reflexive and transitive but not symmetric.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. (i)<\/strong> <img decoding=\"async\" style=\"height: 17px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image062.png\" \/>\u00a0which is true, so <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image042.png\" \/>\u00a0R,\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>(ii) <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image063.png\" \/>\u00a0but <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image064.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p>(iii) <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image063.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image065.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 17px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image066.png\" \/>\u00a0which is true. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is reflexive and transitive but not symmetric.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_Check_whether_the_relation_R_in_R_defined_by_R_is_reflexive_symmetric_or_transitive\"><\/span><strong>5. Check whether the relation R in R defined by R = <img decoding=\"async\" style=\"height: 29px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image067.png\" \/>\u00a0is reflexive, symmetric or transitive.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. (i)<\/strong> For <img decoding=\"async\" style=\"height: 27px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image068.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image069.png\" \/>\u00a0which is false.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p><strong>(ii)<\/strong> For <img decoding=\"async\" style=\"height: 27px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image070.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image071.png\" \/>\u00a0which is false.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p><strong>(iii) <\/strong>For <img decoding=\"async\" style=\"height: 27px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image072.png\" \/><img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image073.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image074.png\" \/>, <img decoding=\"async\" style=\"height: 21px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image075.png\" \/>\u00a0which is false.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<\/p>\n<p>Therefore, R is neither reflexive, nor symmetric and nor transitive.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-2\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Show_that_the_relation_in_the_set_A_1_2_3_given_by_R_1_2_2_1_is_symmetric_but_neither_reflexive_nor_transitive\"><\/span><strong>6. Show that the relation in the set A = {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>R = {(1, 2), (2, 1)}, so for <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image076.png\" \/>, (1, 1) <img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image015.png\" \/>\u00a0R.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p>Also if <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image056.png\" \/>\u00a0then <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image077.png\" \/>\u00a0R<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Now <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image056.png\" \/>\u00a0R and <img decoding=\"async\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image057.png\" \/>\u00a0then does not imply <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image078.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive..<\/p>\n<p>Therefore, R is symmetric but neither reflexive nor transitive.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-3\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Show_that_the_relation_R_in_the_set_A_of_all_the_books_in_a_library_of_a_college_given_by_R_is_an_equivalence_relation\"><\/span><strong>7. Show that the relation R in the set A of all the books in a library of a college, given by R = <img decoding=\"async\" style=\"height: 27px; width: 291px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image079.png\" \/>\u00a0is an equivalence relation.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Books <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0have same number of pages <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image028.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>If <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image021.png\" \/>\u00a0R, so <img decoding=\"async\" style=\"height: 27px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image080.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Now if\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image012.png\" \/>\u00a0R, <img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image031.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image033.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is an equivalence relation.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-4\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_Show_that_the_relation_R_in_the_set_A_1_2_3_4_5_given_by_R_is_an_equivalence_relation_Show_that_all_the_elements_of_1_3_5_are_related_to_each_other_and_all_the_elements_of_2_4_are_related_to_each_other_But_no_element_of_1_3_5_is_related_to_any_element_of_2_4\"><\/span><strong>8. Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = <img decoding=\"async\" style=\"height: 29px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image081.png\" \/>\u00a0is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. \u00a0<\/strong>A = {1, 2, 3, 4, 5} and R = <img decoding=\"async\" style=\"height: 29px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image082.png\" \/>, then R = {(1, 3), (1, 5), (3, 5), (2, 4)}<\/p>\n<p><strong>(a)<\/strong> For <img decoding=\"async\" style=\"height: 27px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image068.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image083.png\" \/>\u00a0which is even. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>If <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image084.png\" \/>\u00a0is even, then <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image085.png\" \/>\u00a0is also even.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>\u00a0R is symmetric.<\/p>\n<p>Now, if <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image084.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image086.png\" \/>\u00a0is even then <img decoding=\"async\" style=\"height: 27px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image087.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image088.png\" \/>is also even.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is an equivalence relation.<\/p>\n<p><strong>(b)<\/strong> Elements of {1, 3, 5} are related to each other.<\/p>\n<p>Since <img decoding=\"async\" style=\"height: 27px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image089.png\" \/>\u00a0all are even numbers<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0Elements of {1, 3, 5} are related to each other.<\/p>\n<p>Similarly elements of (2, 4) are related to each other.<\/p>\n<p>Since <img decoding=\"async\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image090.png\" \/>\u00a0an even number, then no element of the set {1, 3, 5} is related to any element of (2, 4).<\/p>\n<p>Hence no element of {1, 3, 5} is related to any element of {2, 4}.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-5\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_Show_that_each_of_the_relation_R_in_the_set_A_given_by\"><\/span><strong>9. Show that each of the relation R in the set A = <img decoding=\"async\" style=\"height: 27px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image091.png\" \/>\u00a0given by:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(i) R = <img decoding=\"async\" style=\"height: 29px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image092.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) R = <img decoding=\"async\" style=\"height: 27px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image093.png\" \/>\u00a0<\/strong>is an equivalence relation. Find the set of all elements related to 1 in each case.<\/p>\n<p><strong>Ans. (a) (i) <\/strong>A = <img decoding=\"async\" style=\"height: 27px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image094.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>A = {0, 1, 2, 3, \u2026\u2026\u2026.., 12}<\/p>\n<p>Now R = <img decoding=\"async\" style=\"height: 29px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image092.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>\u00a0R = {(4, 0), (0, 4), (5, 1), (1, 5), (6, 2), (2, 6), \u2026.. (12, 9), (9, 12), \u2026. (8, 0), (0, 8), \u2026..\u00a0 (8, 4), (4, 8), \u2026\u2026 (12, 12)}<\/p>\n<p>Here, <img decoding=\"async\" style=\"height: 27px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image095.png\" \/>\u00a0is a multiple of 4.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image096.png\" \/>\u00a0is a multiple of 4. <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Also we observe that <img decoding=\"async\" style=\"height: 27px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image097.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>And <img decoding=\"async\" style=\"height: 27px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image098.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image099.png\" \/>is the multiple of 4.\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Hence R is an equivalence relation.<\/p>\n<p><strong>(ii)<\/strong> R = <img decoding=\"async\" style=\"height: 27px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image093.png\" \/>\u00a0and A = {0, 1, 2, 3, \u2026\u2026\u2026.., 12}<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>\u00a0R = {(0, 0), (1, 1), (2, 2), \u2026\u2026.. (12, 12)}<\/p>\n<p>For <img decoding=\"async\" style=\"height: 27px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image068.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image100.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>As <img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image101.png\" \/>\u00a0then <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image052.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image101.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image102.png\" \/>\u00a0then <img decoding=\"async\" style=\"height: 15px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image103.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Hence R is an equivalence relation.<\/p>\n<p><strong>(b) <\/strong>Now set of all elements related to 1 in each case.<\/p>\n<p><strong>(i) <\/strong>Required set = {1, 5, 9}\u00a0 (ii) Required set = {1}<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-6\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_Give_an_example_of_a_relation_which_is\"><\/span><strong>10. Give an example of a relation, which is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(i) Symmetric but neither reflexive nor transitive.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) Transitive but neither reflexive nor symmetric.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) Reflexive and symmetric but not transitive.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) Reflexive and transitive but not symmetric.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) Symmetric and transitive but not reflexive.<\/strong><\/p>\n<p><strong>Ans. (i)<\/strong> The relation \u201cis perpendicular to\u201d <img decoding=\"async\" style=\"height: 25px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image104.png\" \/>\u00a0is not perpendicular to <img decoding=\"async\" style=\"height: 25px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image105.png\" \/><\/p>\n<p>If <img decoding=\"async\" style=\"height: 25px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image106.png\" \/>\u00a0then <img decoding=\"async\" style=\"height: 25px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image107.png\" \/>, however if <img decoding=\"async\" style=\"height: 25px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image106.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 25px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image108.png\" \/>\u00a0then <img decoding=\"async\" style=\"height: 25px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image104.png\" \/>\u00a0is not perpendicular to <img decoding=\"async\" style=\"height: 25px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image109.png\" \/><\/p>\n<p>So it is clear that R \u201cis perpendicular to\u201d is a symmetric but neither reflexive nor transitive.<\/p>\n<p><strong>(ii)<\/strong> Relation R = <img decoding=\"async\" style=\"height: 27px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image110.png\" \/><\/p>\n<p>We know that <img decoding=\"async\" style=\"height: 15px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image111.png\" \/>\u00a0is false. Also <img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image112.png\" \/>\u00a0but <img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image113.png\" \/>\u00a0is false and if <img decoding=\"async\" style=\"height: 17px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image112.png\" \/>, <img decoding=\"async\" style=\"height: 17px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image114.png\" \/>\u00a0this implies <img decoding=\"async\" style=\"height: 15px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image115.png\" \/><\/p>\n<p>Therefore, R is transitive, but neither reflexive nor symmetric.<\/p>\n<p><strong>(iii)<\/strong> \u201cis friend of\u201d R = <img decoding=\"async\" style=\"height: 27px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image116.png\" \/><\/p>\n<p>It is clear that <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is friend of <img decoding=\"async\" style=\"height: 15px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image117.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is friend of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is friend of <img decoding=\"async\" style=\"height: 15px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image117.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Also if\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is friend of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is friend of <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image036.png\" \/>\u00a0then<\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0cannot be friend of <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image036.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not transitive.<\/p>\n<p>Therefore, R is reflexive and symmetric but not transitive.<\/p>\n<p><strong>(iv) <\/strong>\u201cis greater or equal to\u201d R = <img decoding=\"async\" style=\"height: 27px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image118.png\" \/><\/p>\n<p>It is clear that <img decoding=\"async\" style=\"height: 17px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image119.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>And <img decoding=\"async\" style=\"height: 20px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image120.png\" \/>\u00a0does not imply <img decoding=\"async\" style=\"height: 20px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image121.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p>But <img decoding=\"async\" style=\"height: 20px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image120.png\" \/>, <img decoding=\"async\" style=\"height: 20px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image122.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 17px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image123.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is reflexive and transitive but not symmetric.<\/p>\n<p><strong>(v) <\/strong>\u201cis brother of\u201d R = <img decoding=\"async\" style=\"height: 27px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image124.png\" \/><\/p>\n<p>It is clear that <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is not the brother of <img decoding=\"async\" style=\"height: 15px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image117.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not reflexive.<\/p>\n<p>Also <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is brother of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is brother of <img decoding=\"async\" style=\"height: 15px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image117.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Also if\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0is brother of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image030.png\" \/>\u00a0is brother of <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image036.png\" \/>\u00a0then<\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image029.png\" \/>\u00a0can be brother of <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image036.png\" \/><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is symmetric and transitive but not reflexive.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-7\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_Show_that_the_relation_R_in_the_set_A_of_points_in_a_plane_given_by_R_P_Q_distance_of_the_point_P_from_the_origin_is_same_as_the_distance_of_the_point_Q_from_the_origin_is_an_equivalence_relation_Further_show_that_the_set_of_all_points_related_to_a_point_P_0_0_is_the_circle_passing_through_P_with_origin_as_centre\"><\/span><strong>11. Show that the relation R in the set A of points in a plane given by R = {(P. Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image125.png\" \/>\u00a0(0, 0) is the circle passing through P with origin as centre.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>\u00a0<strong>Part I<\/strong>: R = {(P, Q): distance of the point P from the origin is the same as the distance of the point Q from the origin}<\/p>\n<p>Let P<img decoding=\"async\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image126.png\" \/> and Q<img decoding=\"async\" style=\"height: 27px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image127.png\" \/> and O (0, 0).<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>OP = OQ <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 31px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image128.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 31px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image129.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/><img decoding=\"async\" style=\"height: 25px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image130.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 25px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image131.png\" \/><\/p>\n<p>Now, For (P, P), OP = OP <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Also OP = OQ and OQ = OP <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0(P, Q) = (Q, P)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Also OP = OQ and OQ = OR <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0OP = OQ\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is an equivalent relation.<\/p>\n<p><strong>Part II<\/strong>: As <img decoding=\"async\" style=\"height: 25px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image130.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 25px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image131.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 20px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image132.png\" \/>\u00a0(let) <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image133.png\" \/>\u00a0which represents a circle with centre (0, 0) and radius <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image134.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-8\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_Show_that_the_relation_R_defined_in_the_set_A_of_all_triangles_as_R_T1_T2_T1_is_similar_to_T2_is_equivalence_relation_Consider_three_right_angle_triangles_T1_with_sides_3_4_5_T2_with_sides_5_12_13_and_T3_with_sides_6_8_10_Which_triangles_among_T1_T2_and_T3_are_related\"><\/span><strong>12. Show that the relation R defined in the set A of all triangles as R = {(T<sub>1<\/sub>, T<sub>2<\/sub>) : T<sub>1<\/sub> is similar to T<sub>2<\/sub>}, is equivalence relation. Consider three right angle triangles T<sub>1<\/sub> with sides 3, 4, 5, T2 with sides 5, 12, 13 and T<sub>3<\/sub> with sides 6, 8, 10. Which triangles among T<sub>1<\/sub>, T<sub>2<\/sub> and T<sub>3<\/sub> are related?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> <strong>Part I<\/strong>: R = {(T<sub>1<\/sub>, T<sub>2<\/sub>): T<sub>1<\/sub> is similar to T<sub>2<\/sub>} and T<sub>1<\/sub>, T<sub>2<\/sub> are triangle.<\/p>\n<p>We know that each triangle similar to itself and thus (T<sub>1<\/sub>, T<sub>2<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p>Also two triangles are similar, then T<sub>1<\/sub><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image135.png\" \/>\u00a0T<sub>2<\/sub> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0T<sub>1<\/sub><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image135.png\" \/>\u00a0T<sub>2<\/sub> <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p>Again, if then T<sub>1<\/sub><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image135.png\" \/>\u00a0T<sub>2<\/sub>\u00a0 and then T<sub>2<\/sub><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image135.png\" \/>\u00a0T<sub>3<\/sub> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>then T<sub>1<\/sub><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image135.png\" \/>\u00a0T<sub>3<\/sub> <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p>Therefore, R is an equivalent relation.<\/p>\n<p><strong>Part II<\/strong>: It is given that T<sub>1<\/sub>, T<sub>2<\/sub> and T<sub>3<\/sub> are right angled triangles.<\/p>\n<p><strong><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/><\/strong>T<sub>1<\/sub> with sides 3, 4, 5\u00a0 T<sub>2<\/sub> with sides 5, 12, 13 and<\/p>\n<p>T<sub>3<\/sub> with sides 6, 8, 10<\/p>\n<p>Since, two triangles are similar if corresponding sides are proportional.<\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 41px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image136.png\" \/><\/p>\n<p>Therefore, T<sub>1<\/sub> and T<sub>3<\/sub> are related.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-9\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_Show_that_the_relation_R_defined_in_the_set_A_of_all_polygons_as_R_P1_P2_P1_and_P2_have_same_number_of_sides_is_an_equivalence_relation_What_is_the_set_of_all_elements_in_A_related_to_the_right_angle_triangle_T_with_sides_3_4_and_5\"><\/span><strong>13. Show that the relation R defined in the set A of all polygons as R = {(P<sub>1<\/sub>, P<sub>2<\/sub>) : P<sub>1<\/sub> and P<sub>2<\/sub> have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4, and 5?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. Part I<\/strong>: R = {(P<sub>1<\/sub>, P<sub>2<\/sub>): P<sub>1<\/sub> and P<sub>2<\/sub> have same number of sides}<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Consider the element (P<sub>1<\/sub>, P<sub>2<\/sub>), it shows P<sub>1<\/sub> and P<sub>2<\/sub> have same number of sides. Therefore, R is reflexive.<\/p>\n<p><strong>(ii)<\/strong> If (P<sub>1<\/sub>, P<sub>2<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R then also (P<sub>2<\/sub>, P<sub>1<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>\u00a0(P<sub>1<\/sub>, P<sub>2<\/sub>) = (P<sub>2<\/sub>, P<sub>1<\/sub>) as P<sub>1<\/sub> and P<sub>2<\/sub> have same number of sides, therefore, R is symmetric.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> If (P<sub>1<\/sub>, P<sub>2<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R and (P<sub>2<\/sub>, P<sub>3<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R then also (P<sub>1<\/sub>, P<sub>3<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R as P<sub>1<\/sub>, P<sub>2<\/sub> and P<sub>3<\/sub> have same number of sides, therefore, R is transitive.<\/p>\n<p>Therefore, R is an equivalent relation.<\/p>\n<p style=\"text-align: justify;\"><strong>Part II<\/strong>: we know that if 3, 4, 5 are the sides of a triangle, then the triangle is right angled triangle. Therefore, the set A is the set of right angled triangle.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-10\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_Let_L_be_the_set_of_all_lines_in_XY_plane_and_R_be_the_relation_in_L_defined_as_R_L1_L2_L1_is_parallel_to_L2_Show_that_R_is_an_equivalence_relation_Find_the_set_of_all_lines_related_to_the_line\"><\/span><strong>14. Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L<sub>1<\/sub>, L<sub>2<\/sub>) : L<sub>1<\/sub> is parallel to L<sub>2<\/sub>}. Show that R is an equivalence relation. Find the set of all lines related to the line <img decoding=\"async\" style=\"height: 21px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image137.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. Part I<\/strong>: R = {(L<sub>1<\/sub>, L<sub>2<\/sub>): L<sub>1<\/sub> is parallel to L<sub>2<\/sub>}<\/p>\n<p style=\"text-align: justify;\">(i) It is clear that L<sub>1<\/sub> <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image138.png\" \/>\u00a0L<sub>1<\/sub> i.e., (L<sub>1<\/sub>, L<sub>1<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p style=\"text-align: justify;\">(ii) If L<sub>1<\/sub> <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image138.png\" \/>\u00a0L<sub>2<\/sub> and L<sub>2<\/sub> <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image138.png\" \/>\u00a0L<sub>1<\/sub> then (L<sub>1<\/sub>, L<sub>2<\/sub>)<img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R \u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is symmetric.<\/p>\n<p style=\"text-align: justify;\">(iii) If L<sub>1<\/sub> <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image138.png\" \/>\u00a0L<sub>2<\/sub> and L<sub>2<\/sub> <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image138.png\" \/>\u00a0L<sub>3<\/sub> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a0L<sub>1<\/sub> <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image138.png\" \/>\u00a0L<sub>3<\/sub> <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p style=\"text-align: justify;\">Therefore, R is an equivalent relation.<\/p>\n<p style=\"text-align: justify;\"><strong>Part II<\/strong>: All the lines related to the line <img decoding=\"async\" style=\"height: 21px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image139.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image140.png\" \/>\u00a0where <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image141.png\" \/>\u00a0is a real number.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-11\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_Let_R_be_the_relation_in_the_set_1_2_3_4_given_by_R_1_2_2_2_1_1_4_4_1_3_3_3_3_2_Choose_the_correct_answer\"><\/span><strong>15. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(A) R is reflexive and symmetric but not transitive.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) R is reflexive and transitive but not symmetric.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) R is symmetric and transitive but not reflexive.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) R is an equivalence relation.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.<\/strong> Let R be the relation in the set {1, 2, 3, 4} is given by<\/p>\n<p style=\"text-align: justify;\">R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}<\/p>\n<p style=\"text-align: justify;\"><strong>(a)<\/strong> (1, 1), (2, 2), (3, 3), (4, 4) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R \u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is reflexive.<\/p>\n<p style=\"text-align: justify;\"><strong>(b) <\/strong>(1, 2) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R but (2, 1) <img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image015.png\" \/>\u00a0R\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is not symmetric.<\/p>\n<p style=\"text-align: justify;\"><strong>(c)<\/strong> If (1, 3) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R and (3, 2) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R then (1, 2) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R \u00a0<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image011.png\" \/>R is transitive.<\/p>\n<p style=\"text-align: justify;\">Therefore, option (B) is correct.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-12\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_Let_R_be_the_relation_in_the_set_N_given_by_R_Choose_the_correct_answer\"><\/span><strong>16. Let R be the relation in the set N given by R = <img decoding=\"async\" style=\"height: 27px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image142.png\" \/>\u00a0Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(A) (2, 4) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) (3, 8) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) (6, 8) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) (8, 7) <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image014.png\" \/>\u00a0R<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.<\/strong> Given: <img decoding=\"async\" style=\"height: 21px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image143.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(A)<\/strong> <img decoding=\"async\" style=\"height: 21px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image144.png\" \/>, Here <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image145.png\" \/>\u00a0is not true, therefore, this option is incorrect.<\/p>\n<p style=\"text-align: justify;\"><strong>(B)<\/strong> <img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image146.png\" \/>and <img decoding=\"async\" style=\"height: 19px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image147.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image148.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a03 = 6, which is false.<\/p>\n<p style=\"text-align: justify;\">Therefore, this option is incorrect.<\/p>\n<p style=\"text-align: justify;\"><strong>(C)<\/strong> <img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image149.png\" \/>and <img decoding=\"async\" style=\"height: 19px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image147.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image150.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a06 = 6, which is true.<\/p>\n<p style=\"text-align: justify;\">Therefore, option (C) is correct.<\/p>\n<p style=\"text-align: justify;\"><strong>(D) <\/strong><img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image151.png\" \/>and <img decoding=\"async\" style=\"height: 19px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image147.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image152.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex1.1\/image032.png\" \/>\u00a08 = 5, which is false.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_11-13\"><\/span>NCERT Solutions class 12 Maths Exercise 1.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes textbook solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Students\"><\/span>CBSE App for Students<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Exercise 1.1\u00a0solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT textbooks. Class 12 Maths chapter wise NCERT solution for &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 1.1\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-1-1\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 1.1\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4459","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Exercise 1.1 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 1.1 in PDF format for free download. 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