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)