Set Theory Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Question : 1

Consider the following for the next three (03) items : In a certain town of population size 1,00,000 three types of newspapers (I, II and III) are available. The percentages of the people in the town who read these papers are as follows :

a) 66, 000

b) 64, 000

c) 62, 000

d) 68, 000

Question : 2

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

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}}}

Question : 4

Let A and B be finite non-empty sets with the number of elements in A = m and number of elements in B = n. Let m > n. If for some integer k ≥ 1, the number of nonempty subsets of A = $2^k$ + the number of non-empty subsets of B, then which one of the following is correct?

a) m = n + p for some odd prime number p

b) m = n + 1

c) m = n + 2

d) m = n + t for some composite number t

Question : 5

In an examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% candidates failed in both English and Mathematics, what percentage of candidates passed in both the subjects?

a) 23%

b) 21%

c) 18%

d) 25%

Question : 6

Let A = {7, 8, 9, 10, 11, 12} and B = {7, 10, 14, 15}. What is the number of elements in (A–B) and (B–A) respectively ?

a) 2 and 2

b) 4 and 2

c) 2 and 4

d) 4 and 4