## NCERT Solutions for Class 11 Maths Chapter 1 – Sets Ex 1.5

#### Question 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)
(ii)
(iii)
(iv)
(v)
(vi)

U ={1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3, 4}
B = {2, 4, 6, 8}
C = {3, 4, 5, 6}
(i)
(ii)
(iii)
(iv)
(v)
(vi)

#### Question 2:

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {fgha}

U = {a, b, c, d, e, f, g, h}
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {fgha}

#### Question 3:

Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i) {xx is an even natural number}
(ii) {xx is an odd natural number}
(iii) {xx is a positive multiple of 3}
(iv) {xx is a prime number}
(v) {xx is a natural number divisible by 3 and 5}
(vi) {xx is a perfect square}
(vii) {xx is perfect cube}
(viii) {xx + 5 = 8}
(ix) {x: 2x + 5 = 9}
(x) {xx ≥ 7}
(xi) {xx ∈ N and 2x + 1 > 10}

U = N: Set of natural numbers
(i) {xx is an even natural number}´ = {xx is an odd natural number}
(ii) {xx is an odd natural number}´ = {xx is an even natural number}
(iii) {xx is a positive multiple of 3}´ = {xx ∈ N and x is not a multiple of 3}
(iv) {xx is a prime number}´ ={xx is a positive composite number and x = 1}
(v) {xx is a natural number divisible by 3 and 5}´ = {xx is a natural number that is not divisible by 3 or 5}
(vi) {xx is a perfect square}´ = {xx ∈ N and is not a perfect square}
(vii) {xx is a perfect cube}´ = {xx ∈ N and is not a perfect cube}
(viii) {xx + 5 = 8}´ = {xx ∈ N and x ≠ 3}
(ix) {x: 2x + 5 = 9}´ = {xx ∈ N and x ≠ 2}
(x) {xx ≥ 7}´ = {xx ∈ N and x < 7}
(xi) {xx ∈ N and 2x + 1 > 10}´ = {xx ∈ N and ≤ 9/2}

#### Question 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
(i)  (ii)

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8}, B = {2, 3, 5, 7}
(i)
(ii)

#### Question 5:

Draw appropriate Venn diagram for each of the following:
(i)
(ii)
(iii)
(iv)

(i)
(ii)
(iii)
(iv)

#### Question 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 60°, what is?

is the set of all equilateral triangles.

#### Question 7:

Fill in the blanks to make each of the following a true statement:
(i)
(ii) Φ′ ∩ A = …
(iii)
(iv)