NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5

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

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5 are the part of NCERT Solutions for Class 11 Maths. In this post, you will find the NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5.

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

#### Ex 1.5 Class 11 Maths 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) A’
(ii) B’
(iii) (A
C)’
(iv) (A
B)’
(v) (A’)’
(vi) (B – C)’

Solution.
Here 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}
(i) A’= U – A
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4}
= {5, 6, 7, 8, 9}

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

(iii) A C = {1, 2, 3, 4} {3, 4, 5, 6}
= (1, 2, 3, 4, 5, 6}
(A
C)’ = U – (A C)
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4, 5, 6}
= {7, 8, 9}

(iv) A B = {1, 2, 3, 4} {2, 4, 6, 8}
= {1, 2, 3, 4, 6, 8}
(A
B)’ = U – (A B)
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4, 6, 8}
= {5, 7, 9}

(v) We know that A’ = {5, 6, 7, 8, 9}
(A’)’ = U – A’
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {5, 6, 7, 8, 9}
= {1, 2, 3, 4}

(vi) B – C = {2, 4, 6, 8} – {3, 4, 5, 6} = {2, 8}
(B – C)’ = U – (B – C)
= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 8}
= {1, 3, 4, 5, 6, 7, 9}.

#### Ex 1.5 Class 11 Maths 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 = {f, g, h, a}

Solution.
(i) A’ = U – A = {a, b, c, d, e, f, g, h} – {a, b, c}
= {d, e, f, g, h}

(ii) B’ = U – B = {a, b, c, d, e, f, g, h} – {d, e, f, g}
= {a, b, c, h}

(iii) C’ = U – C = {a, b, c, d, e, f, g, h} – {a, c, e, g}
= {b, d, f, h}

(iv) D’ = U – D = {a, b, c, d, e, f, g, h} – {f, g, h, a}
= {b, c, d, e}

#### Ex 1.5 Class 11 Maths Question 3.

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

Solution.

#### Ex 1.5 Class 11 Maths 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)
(A
B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’
B’

Solution.

#### Ex 1.5 Class 11 Maths Question 5.

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

Solution.

#### Ex 1.5 Class 11 Maths 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 A’?

Solution.
Here U = {x: x is a triangle}
A = {x: x is a triangle and has at least one angle different from 60°}
A’ = U – A = {x: x is a triangle} – {x: x is a triangle and has at least one angle different from 60°}
= {x: x is a triangle and has all angles equal to 60°}
= {x: x is an equilateral triangle}

#### Ex 1.5 Class 11 Maths Question 7.

Fill in the blanks to make each of the following a true statement:
(i) A
A’ = …….
(ii) Ï†’ ∩ A = …….
(iii) A ∩ A’ = …….
(iv) U’ ∩ A = …….

Solution.
(i) A
A’= U
(ii) Ï†’ ∩ A = U ∩ A = A
(iii) A ∩ A’ = Ï†
(iv) U’ ∩ A = Ï† ∩ A = Ï†