**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:**A = {a, b, c}**

**(i)****(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:**{x: x is an even natural number}**

**(i)****(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**(A ∪ B)’ = A’ ∩ B’**

**(i)****(ii)**(A ∩ B)’ = A’ ∪ B’

**Solution.**

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

Draw
appropriate Venn diagram for each of the following:**(A ∪ B)’**

**(i)****(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†

**Related Links:**

**NCERT Solutions for Maths Class 9**