Set Theory Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 2 EXERCISES
The following question based on Set Theory topic of quantitative aptitude
B = {x : x is a natural number and multiple of 5} and
C = {x : x is a natural number and multiple of 10},
then what is the value of A ∩ (B ∪ C)?
(a) {2, 4, 6, ...}
(b) {5, 10, 15, 20, ...}
(c) {10, 20, 30, ...}
(d) {20, 40, 60, ...}
The correct answers to the above question in:
Answer: (c)
We know that
A ∩ (B ∪ C) = {A ∩ B) ∪ (A ∩ C)
Example:
A = Set of an even natural number
A = {2, 4, 6, 8, 10, 12, ...}
B = Set of natural number and multiples of 5.
B = {5, 10, 15, 20, 25, ...}
C = Set of natural number and multiple of 10.
C = {10, 20, 30, 40, 50, ...}
A ∩ B = {2, 4, 6, 8, 10, 12, ...} ∩ {5, 10, 15, 20, 25, ...} = {10, 20, 30, ...}
A ∩ C = {2, 4, 6, 8, 10, 12, ...} ∩ {10, 20, 30, 40, 50, ...} = {10, 20, 30, 40, ...}
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
= {10, 20, 30, ...} ∪ {10, 20, 30, 40, ...}
= {10, 20, 30, 40, ...}
Discuss Form
Read more model question set 2 Based Quantitative Aptitude Questions and Answers
Question : 1
In a class of 60 boys, there are 45 boys who play chess and 30 boys who plays carrom. If every boy of the class plays at least one of the two games, then how many boys play carrom only?
a) 15
b) 20
c) 30
d) 10
Answer »Answer: (a)
Total number of boys in the class
n(A ∪ B) = 60
Number of boy play chess n(A) = 45
Number of boy play carrom n(B) = 30
∴ Number of boy play both chess and Carrom
n(A ∩ B) = n(A) + n(B) – n(A ∪ B) = 45 + 30 – 60 = 15
Number of boys plays only carrom n(B) – n(A ∩ B)
= 30 – 15 = 15
42.
Question : 2
Which one of the following is a correct statement?
a) {x : x + 5 = 5} = 0
b) {x : x + 5 = 5} = {0}
c) {x : x + 5 = 5} = Φ
d) {x : x + 5 = 5} = {Φ}
Answer »Answer: (b)
Solving the given equation for x, we have
x + 5 = 5 ⇒ x = 5 – 5 = 0
Therefore, in the given set we have only one element i.e. 0. Element Φ is a null set i.e. no elements in the set.
Hence, option (b) is the correct answer.
Question : 3
Which one of the following is correct?
a) Φ ε {{Φ}, {{Φ}}}
b) {Φ} ε {{Φ}, {{Φ}}}
c) {Φ} ⊂ {{Φ}, {{Φ}}}
d) Φ = {{Φ}, {{Φ}}}
Answer »Answer: (b)
Here, {Φ} is an element of {Φ} ε {{Φ}, {{Φ}}}.
Question : 4
If A = {x : $x^2$ – 6x + 8 = 0} and B = {x : $2x^2$ + 3x – 2 = 0} Then, which one of the following is correct?
a) Neither A ⊆ B nor B ⊆ A
b) B ⊆ A
c) A ⊆ B
d) A = B
Answer »Answer: (a)
Given, A ≡ $x^2$ – 6x + 8 = 0
⇒ (x – 4) (x – 2) = 0
⇒ x = 4, 2
and B ≡ $2x^2$ + 3x – 2 = 0
⇒ (2x – 1) (x + 2) = 0
⇒ x = $1/2$ , –2
Hence, neither A ⊆ B nor B ⊆ A.
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