## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) If A, B are two sets, then A ∪ B = …………..

(ii) If A, B are two sets, then A ∩ B = …………..

(iii) If A, B are two sets, then A – B = …………..

(iv) A and B are disjoint sets if and only if A ∩ B = …………..

(v) A and B are overlapping sets if and only if A ∩ B = …………..

(vi) The set {x: x ϵ W, x < 3} in the roster form = …………..

(vii) If A is any set, then A ∪ ϕ = and A ∪ ξ = …………..

(viii) If ξ = {all digits in our number system] and A ={1,2, 3, 4, 5}, then A’= …………..

(ix) If A is any set and A’ is its complement, then A ∪ A’ = and A ∩ A’ = …………..

Solution:

(i) If A, B are two sets, then A ∪ B = {x |x ϵ A or x ϵ B}.

(ii) If A, B are two sets, then A ∩ B = {x| x ϵ A or x ϵ B}.

(iii) If A, B are two sets, then A – B = {x|x ϵ A or x ∉ B}.

(iv) A and B are disjoint sets if and only if A ∩ B = ϕ

(v) A and B are overlapping sets if and only if A ∩ B = ϕ.

(vi) The set {x: x ϵ W, x < 3} in the roster form = {0, 1, 2}.

(vii) If A is any set, then A ∪ ϕ = A and A ∪ ξ = ξ.

(viii)If ξ = {all digits in our number system]

and A = {1, 2, 3, 4, 5}, then A’ = {0, 6, 7, 8, 9}.

(ix) If A is any set and A’ is its complement,

then A ∪ A’ = ξ and A ∩ A’ = ϕ

Question 2.

State whether the following statements are true (T) or false (F):

(i) If ξ is the universal set and A is any set, then A’ = {x; x ϵ ξ and r ∉ A}.

(ii) If A = {0,1,2,3,4, 5} and B = {0,3, 5, 7}, then A ∩ B = B.

(in) If A= {0,1, 2,3,4, 5} and B = {0,3,5,7}, then A ∪ B=A.

(iv) If ξ = {all digits in our number system}, A = {multiples of 2} and B = {multiples of 3}, then A ∩ B = {6}.

Solution:

(i) If 4 is the universal set and A is any set,

then A’ = {x ; x ϵ ξ, and x ∉ A}. True

(ii) If A= {0, 1, 2, 3, 4, 5} and B = {0, 3, 5, 7}, then A n B = B. False

Correct:

As A n B = {0, 1,3, 5}

(iii) If A = {0, 1, 2, 3, 4, 5} and B = {0, 3, 5, 7}, then A ∪ B = A. False

Correct:

As A ∪ B = {0, 1, 2, 3, 4, 5, 7}

(iv) If ξ = {all digits in our number system}, A = {multiples of 2}

and B = {multiples of 3}, then A ∩ B = {6}. True

If ξ = {all digits in our number system}

= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {multiples of 2} = {2, 4, 6, 8}

B = {multiples of 3} = {3, 6, 9}

Then A ∩ B = {6}

**Multiple Choice Questions**

**Choose the correct answer from the given four options (3 to 12):**

Question 3.

If A = {x | x is a colour of rainbow} and B = {white, red, green}, then A ∩ B is

(a) B

(b) {green}

(c) {red}

(d) {green, red}

Solution:

A = {x | x is a colour of rainbow}

= {red, green, blue, voilet, yellow, Indigo, orange}

B = {white, red, green}

A ∩ B = {red, green} (d)

Question 4.

If P = {-1, 0, 1, 2, 5} and Q = {3, 5, 7}, then P ∪ Q is

(a) {5}

(b) {-1, 0, 1, 2, 3, 7}

(c) {-1, 0, 1, 2, 3, 5, 7}

(d) none of these

Solution:

P = {-1, 0, 1, 2, 5}

Q = {3, 5, 7}

∴ P ∪ Q = {0, 1, 2, 3, 5, 7} (c)

Question 5.

If A and B are two sets, then A – B is defined as

(a) {x |x ϵ A or x ϵ B}

(b) {x | x ϵ A and x ϵ B}

(c) {x | x ϵ A and x ∉ B}

(d) {x | x ϵ B and x ∉ A}

Solution:

A and B are two sets

∴ A – B = {x |x ϵ A and x ∉ B} (c)

Question 6.

If A is any set, then A ∪ ϕ is

(a) A

(b) ϕ

(c) 2,

(d) none of these

Solution:

A ∪ ϕ = A

Where A is any set. (a)

Question 7.

A ∩ ξ is same as

(a) A

(b) ϕ

(c) A’

(d) ξ

Solution:

A ∩ ξ = A (a)

Question 8.

If ξ = W and A = {x | x ϵ W and x ≤ 10}, then A’ is

(a) ϕ

(b) {x | x ϵ W and 0 ≤ x ≤ 10}

(c) {x | x ϵ W and x ≤ 10}

(d) {x | x ϵ W and x ≥ 11}

Solution:

ξ = W, A = {x | x ϵ W and x ≤ 10}

= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

∴ A’ = {x | x ϵ W, and x ≥ 11} (d)

Question 9.

If ξ= {x | x ϵ W, x ≤ 12}, A – {x | x is a multiple of 3} and B = {x | x is a multiple of 4}, then A ∩ B is

(a) ϕ

(b) {0}

(c) {12}

(d) {0, 12}

Solution:

A = (x | x is a multiple of 3}

= {0, 3, 6, 9, 12}

B = {x | x is a multiple of 4}

= {0, 4, 8, 12}

∴ A ∩ B = {0, 12} (d)

Question 10.

If ξ = (all digits in our number system}, A = {x | x is prime} and B = {x | x is even}, then B – A is

(a) {4, 6, 8}

(b) {0, 4, 6, 8}

(c) {3, 5, 7}

(d) {2}

Solution:

ξ = {all digits in our number system}

= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {x | x is prime}

= {2, 3, 5, 7}

B = {x | x is even}

= {0, 2, 4, 6, 8}

B – A = {0, 4, 6, 8} (b)

Question 11.

If A and B are two sets such that n(A) = 22, n(B) = 18 and n(A ∪ B) = 35, then n(A ∩ B)

(a) 4

(b) 5

(c) 15

(d) 75

Solution:

n(A) = 22, n(B) = 18

n(A ∪ B) = 35

n( A ∪ B) = n(A) + n( B) – n(A ∩ B)

35 = 22 + 18 – n(A ∩ B)

n(A ∩ B) = 40 – 35 = 5 (b)

Question 12.

In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of person who read neither is

(a) 180

(b) 210

(c) 260

(d) 290

Solution:

Total number of person = 840

Person who read Hindi = 450

⇒ n(A) = 450

Person who read English = 300

⇒ n(B) = 300

Person who read both = 200

⇒ n(A ∩ B) = 200

Now, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

= 450 + 300 – 200

= 750 – 200 = 550

∴ Person who read neither = 840 – 550 = 290 (d)