{"id":4583,"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-1-5\/"},"modified":"2016-05-17T10:35:44","modified_gmt":"2016-05-17T05:05:44","slug":"ncert-solutions-class-11-maths-exercise-1-5","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-1-5\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 1.5"},"content":{"rendered":"

Exercise 1.5<\/strong><\/p>\n

1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find:<\/strong><\/p>\n

(i) A\u2019 <\/strong><\/p>\n

(ii) B\u2019 <\/strong><\/p>\n

(iii) (A C)\u2019 <\/strong><\/p>\n

(iv) (A B)\u2019<\/strong><\/p>\n

(v) (A\u2019)\u2019 <\/strong><\/p>\n

(vi) (B \u2013 C)\u2019<\/strong><\/p>\n

Ans.<\/strong> Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9},<\/p>\n

A = {1, 2, 3, 4},<\/p>\n

B = {2, 4, 6, 8} and C = {3, 4, 5, 6}.<\/p>\n

(i) <\/strong>A\u2019 = U \u2013 A = {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {1, 2, 3, 4}<\/p>\n

= {5, 6, 7, 8, 9}<\/p>\n

(ii) <\/strong>B\u2019 = U \u2013 B = {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 4, 6, 8}<\/p>\n

= {1, 3, 5, 7, 9}<\/p>\n

(iii) <\/strong>(A C)\u2019 = U \u2013 (A C)<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 ({1, 2, 3, 4} {3, 4, 5, 6})<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {1, 2, 3, 4, 5, 6} = {7, 8, 9}<\/p>\n

(iv) <\/strong>(A B)\u2019 = U \u2013 (A B)<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 ({1, 2, 3, 4} {2, 4, 6, 8})<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {1, 2, 3, 4, 6, 8} = {5, 7, 9}<\/p>\n

(v) <\/strong>(A\u2019)\u2019 = U \u2013 A\u2019 = U \u2013 (U \u2013 A)<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 ({1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {1, 2, 3, 4})<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {5, 6, 7, 8, 9}<\/p>\n

= {1, 2, 3, 4} = A<\/p>\n

(vi) <\/strong>(B \u2013 C)\u2019 = U \u2013 (B \u2013 C)<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 ({2, 4, 6, 8} \u2013 {3, 4, 5, 6})<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 8}<\/p>\n

= {1, 3, 4, 5, 6, 7, 9}<\/p>\n

\n

2. If U = <\/strong> find the complement of the following sets:<\/strong><\/p>\n

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

(ii) B = <\/strong><\/p>\n

(iii) C = <\/strong><\/p>\n

(iv) D = <\/strong><\/p>\n

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

(i) <\/strong>A\u2019 = U \u2013 A<\/p>\n

= <\/p>\n

(ii) <\/strong>B\u2019 = U \u2013 B<\/p>\n

= <\/p>\n

(iii) <\/strong>C\u2019 = U \u2013 C<\/p>\n

= <\/p>\n

(iv) <\/strong>D\u2019 = U \u2013 D<\/p>\n

= <\/p>\n

\n

3. Taking the set of natural numbers as the universal set, write down the complement of the following set:<\/strong><\/p>\n

(i) {<\/strong> is an even natural number}<\/strong><\/p>\n

(ii) {<\/strong> is an odd natural number}<\/strong><\/p>\n

(iii) {<\/strong> is a positive multiple of 3}<\/strong><\/p>\n

(iv) {<\/strong> is a prime number}<\/strong><\/p>\n

(v) {<\/strong> is a natural number divisible by 3 and 5}<\/strong><\/p>\n

(vi) {<\/strong> is a perfect square}<\/strong><\/p>\n

(vii) {<\/strong> is a perfect cube}<\/strong><\/p>\n

(viii) {<\/strong> + 5 = 8}<\/strong><\/p>\n

(ix) {<\/strong> +5=9}<\/strong><\/p>\n

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

(xi) {<\/strong> N and <\/strong>}<\/strong><\/p>\n

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

(i) <\/strong>Let A = { is an even natural number}<\/p>\n

A\u2019 = U \u2013 A = \u2013 { is an even natural number}<\/p>\n

= { is an odd natural number}<\/p>\n

(ii) <\/strong>Let A = { is an odd natural number}<\/p>\n

A\u2019 = U \u2013 A = \u2013 { is an odd natural number}<\/p>\n

= { is an even natural number}<\/p>\n

(iii) <\/strong>Let A = { is a positive multiple of 3}<\/p>\n

A\u2019 = U \u2013 A = \u2013 { is a positive multiple of 3}<\/p>\n

= { is not a positive multiple of 3}<\/p>\n

(iv) <\/strong>Let A = { is a prime number}<\/p>\n

A\u2019 = U \u2013 A = \u2013 { is a prime number}<\/p>\n

= { is not a prime number}<\/p>\n

(v) <\/strong>Let A = { is a natural number divisible by 3 and 5}<\/p>\n

A\u2019 = U \u2013 A = \u2013 { is a natural number divisible by 15}<\/p>\n

= { is not divisible by 15}<\/p>\n

(vi) <\/strong>Let A = { is a perfect square}<\/p>\n

A\u2019 = U \u2013 A = \u2013 { is a perfect square}<\/p>\n

= { is not a perfect square}<\/p>\n

(vii) <\/strong>Let A = { is a perfect cube}<\/p>\n

A\u2019 = U \u2013 A = \u2013 { is a perfect cube}<\/p>\n

= { is not a perfect cube}<\/p>\n

(viii) <\/strong>Let A = { + 5 = 8} = {3}<\/p>\n

A\u2019 = U \u2013 A = \u2013 {3}<\/p>\n

= { 3}<\/p>\n

(ix) <\/strong>Let A = { +5=9} = {2}<\/p>\n

A\u2019 = U \u2013 A = \u2013 {2}<\/p>\n

= { 2}<\/p>\n

(x) <\/strong>Let A = = {7, 8, 9, 10, \u2026\u2026\u2026}<\/p>\n

A\u2019 = U \u2013 A = \u2013 {7, 8, 9, 10, \u2026\u2026\u2026}<\/p>\n

={1, 2, 3, 4, 5, 6} = { 7}<\/p>\n

(xi) <\/strong>Let A = { N and } = {5, 6, 7, 8, \u2026\u2026\u2026..}<\/p>\n

A\u2019 = U \u2013 A = \u2013 {5, 6, 7, 8, \u2026\u2026\u2026..}<\/p>\n

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

\n

4. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}, verify that:<\/strong><\/p>\n

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

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

Ans. <\/strong>Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9},<\/p>\n

A = {2, 4, 6, 8} and B = {2, 3, 5, 7}<\/p>\n

(i) <\/strong>L.H.S. = = U \u2013 (A B)<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 ({2, 4, 6, 8} {2, 3, 5, 7})<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 3, 4, 5, 6, 7, 8} = {1, 9}<\/p>\n

R.H.S. = = (U \u2013 A) (U \u2013 B)<\/p>\n

= ({1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 4, 6, 8}) ({1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 3, 5, 7})<\/p>\n

= {1, 3, 5, 7, 9} {1, 4, 6, 8, 9} = {1, 9}<\/p>\n

L.H.S. = R. H. S.<\/p>\n

<\/p>\n

(ii) <\/strong>L.H.S. = <\/p>\n

= U \u2013 (A B)<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 ({2, 4, 6, 8} {2, 3, 5, 7})<\/p>\n

= {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2}<\/p>\n

= {1, 3, 4, 5, 6, 7, 8, 9}<\/p>\n

R.H.S. = = (U \u2013 A) (U \u2013 B)<\/p>\n

= ({1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 4, 6, 8}) ({1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 3, 5, 7})<\/p>\n

= {1, 3, 5, 7, 9} {1, 4, 6, 8, 9}<\/p>\n

= {1, 3, 4, 5, 6, 7, 8, 9}<\/p>\n

L.H.S. = R. H. S.<\/p>\n

<\/p>\n

\n

5. Draw appropriate Venn diagrams for each of the following:<\/strong><\/p>\n

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

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

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

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

Ans. (i) <\/strong>In the diagrams, shaded portion represents <\/p>\n

<\/p>\n

(ii) <\/strong>In the diagrams, shaded portion represents <\/p>\n

<\/p>\n

(iii) <\/strong>In the diagrams, shaded portion represents <\/p>\n

<\/p>\n

(iv) <\/strong>In the diagrams, shaded portion represents <\/p>\n

<\/p>\n

\n

6. Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from <\/strong> what is A\u2019?<\/strong><\/p>\n

Ans. <\/strong>Given: U = { is a triangle}<\/p>\n

A = { is a triangle and has at least one angle different from }<\/p>\n

A\u2019 = U \u2013 A = { is a triangle and has all angles equal to }<\/p>\n

= Set of all equilateral triangles<\/p>\n

\n

7. Fill in the blanks to make each of the following a true statement:<\/strong><\/p>\n

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

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

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

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

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

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

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

(iv)<\/strong> <\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 1.5 1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find: (i) A\u2019 (ii) B\u2019 (iii) (A C)\u2019 (iv) (A B)\u2019 (v) (A\u2019)\u2019 (vi) (B \u2013 C)\u2019 Ans. Given: U = … 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],"tags":[],"class_list":["post-4583","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 1.5 | 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-1-5\/\" \/>\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 1.5 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 1.5 1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find: (i) A\u2019 (ii) B\u2019 (iii) (A C)\u2019 (iv) (A B)\u2019 (v) (A\u2019)\u2019 (vi) (B \u2013 C)\u2019 Ans. Given: U = ... 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