{"id":4573,"date":"2016-05-17T09:49:00","date_gmt":"2016-05-17T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-2-1\/"},"modified":"2016-05-17T10:14:26","modified_gmt":"2016-05-17T04:44:26","slug":"ncert-solutions-class-11-maths-exercise-2-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-2-1\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 2.1"},"content":{"rendered":"

Exercise 2.1<\/strong><\/p>\n

1. If <\/strong> find the values of <\/strong> and <\/strong><\/p>\n

Ans. <\/strong>Here <\/p>\n

and <\/p>\n

and <\/p>\n

and <\/p>\n

and <\/p>\n

\n

2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A <\/strong> B).<\/strong><\/p>\n

Ans. <\/strong>Number of elements in set A = 3 and Number of elements in set B = 3<\/p>\n

Number of elements in A <\/strong> B = 3 <\/strong> 3 = 9<\/p>\n

\n

3. If G = {7, 8} and H = {5, 4, 2}, find G <\/strong> H and H <\/strong> G.<\/strong><\/p>\n

Ans. <\/strong>Given: G = {7, 8} and H = {5, 4, 2}<\/p>\n

G<\/strong>H = {(7, 5), (7, 4), (7, 2), (8, 5), (8, 4), (8, 2)}<\/p>\n

And H <\/strong> G = {(5, 7), (4, 7), (2, 7), (5, 8), (4, 8), (2, 8)}<\/p>\n

\n

4. State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly:<\/strong><\/p>\n

(i) If P = <\/strong> and Q = <\/strong> then P <\/strong> Q = <\/strong><\/p>\n

(ii) If A and B are non-empty sets, then A <\/strong> B is a non-empty set of ordered pairs <\/strong> such that <\/strong> A and <\/strong> B.<\/strong><\/p>\n

(iii) If A = {1, 2}, B = {3, 4}, then <\/strong><\/p>\n

Ans. (i)<\/strong> Here P = and Q = <\/p>\n

Number of elements in set P = 2 and Number of elements in set Q = 2<\/p>\n

Number of elements in P <\/strong> Q = 2 <\/strong> 2 = 4<\/p>\n

But P<\/strong>Q = and here number of elements in P <\/strong> Q = 2<\/p>\n

Therefore, statement is false.<\/p>\n

(ii)<\/strong> True<\/p>\n

(iii)<\/strong> True<\/p>\n

\n

5. If A = <\/strong> find A <\/strong> A <\/strong> A.<\/strong><\/p>\n

Ans. <\/strong>Here A = <\/p>\n

A <\/strong>A = <\/p>\n

A <\/strong> A <\/strong> A = <\/p>\n

\n

6. If A <\/strong> B = <\/strong> find A and B.<\/strong><\/p>\n

Ans. <\/strong>Given: A <\/strong> B = <\/p>\n

A = set of first elements = and B = set of second elements = <\/p>\n

\n

7. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:<\/strong><\/p>\n

(i) <\/strong><\/p>\n

(ii) A <\/strong> C is a subset of B <\/strong> D.<\/strong><\/p>\n

Ans. <\/strong>Given: A = {1, 2}, B = {1, 2, 3, 4}, C<\/p>\n

= {5, 6} and D = {5, 6, 7, 8}<\/p>\n

(i)<\/strong> = {1, 2, 3, 4} {5, 6} = <\/p>\n

\u2026\u2026\u2026.(i)<\/p>\n

A <\/strong> B = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4)}<\/p>\n

A <\/strong> C = {(1, 5), (1, 6), (2, 5), (2, 6)<\/p>\n

(A<\/strong>B) (A <\/strong> C) = \u2026\u2026\u2026.(ii)<\/p>\n

Therefore, from eq. (i) and (ii), <\/p>\n

= (A <\/strong> B) (A <\/strong> C)<\/p>\n

(ii)<\/strong> A <\/strong> C = {(1, 5), (1, 6), (2, 5), (2, 6)<\/p>\n

B <\/strong> D = {(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8),<\/p>\n

(4, 5), (4, 6), (4, 7), (4, 8),<\/p>\n

Therefore, it is clear that each element of A <\/strong> C is present in B <\/strong> D.<\/p>\n

A <\/strong> C B <\/strong> D<\/p>\n

\n

8. Let A = {1, 2} and B = {3, 4}, write A B. How many sub sets will A B have? List them.<\/strong><\/p>\n

Ans. <\/strong>Given: A = {1, 2} and B = {3, 4}<\/p>\n

A <\/strong> B = {(1, 3), (1, 4), (2, 3), (2, 4)}<\/p>\n

Number of elements in A <\/strong> B = 4<\/p>\n

Therefore, Number of subsets of A<\/strong>B = = 16<\/p>\n

The subsets are:<\/p>\n

{(1, 3)}, {(1, 4)}, {(2, 3)}, {(2, 4)}, {(1, 3), (1, 4)}, {(1, 3), (2, 3)}, {(1, 3), (2, 4)}, {(1, 4), (2, 3)}<\/p>\n

{(1, 4), (2, 4)}, {(2, 3), (2, 4)}, {(1, 3), (1, 4), (2, 3)}, {(1, 3), (1, 4), (2, 4)}, {(1, 3), (2, 3), (2, 4)},<\/p>\n

{(1, 3), (2, 3), (2, 4)}, {(1, 3), (1, 4), (2, 3), (2, 4)}<\/p>\n

\n

9. Let A and B be two sets such that <\/strong> and <\/strong> If <\/strong> are in A <\/strong> B.<\/strong><\/p>\n

Ans. <\/strong>Here <\/p>\n

A and B<\/p>\n

<\/p>\n

A and B<\/p>\n

<\/p>\n

A and B<\/p>\n

But it is given that and <\/p>\n

A = and B = {1, 2}<\/p>\n

\n

10. The Cartesian Product A <\/strong> A has 9 elements among which are found <\/strong> and (0, 1). Find the set A and the remaining elements of A <\/strong> A.<\/strong><\/p>\n

Ans. <\/strong>Here <\/p>\n

A and A<\/p>\n

<\/p>\n

A and A<\/p>\n

A<\/p>\n

But it is given that which implies that <\/p>\n

A = <\/p>\n

And A <\/strong> A = <\/p>\n

Therefore, the remaining elements of A <\/strong> A are<\/p>\n

and <\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 2.1 1. If find the values of and Ans. Here and and and and 2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A B). Ans. Number of elements in set A = 3 and Number of elements in set … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281,1],"tags":[],"class_list":["post-4573","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions","category-uncategorized"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 2.1 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-2-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 2.1 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 2.1 1. If find the values of and Ans. Here and and and and 2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A B). Ans. Number of elements in set A = 3 and Number of elements in set ... 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