Set Theory Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Question : 1

In a gathering of 100 people, 70 of them can speak Hindi, 60 can speak English and 30 can speak French Further, 30 of them can speak both Hindi and English. 20 can speak both Hindi and French. If x is the number of people who can speak both English and French, then which one of the following is correct? (Assume that everyone can speak at least one of the three languages)

a) x = 9

b) 0 ≤ x < 8

c) 9 < x ≤ 30

d) x = 8

Question : 2

The set {2, 4, 16, 256, ...} can be represented as which one of the following?

a) {x ε N| x = $2^{4n}$ , n = 0, 1, 2, ..}

b) {x ε N | x = $2^2^n$, n = 0,1, 2, ...}

c) {x ε N | x = $2^2^n$ , n ε N }

d) {x ε N| x = $2^{2n}$, n = 0, 1, 2....}

Question : 3

What is {[(A ∪ B)' ∩ A]} - (A - B) equal to?

a) B

b) A

c) Φ

d) B'

Question : 4

Consider the following for the next 04 (four) items that follow : In an examination of Class XII, 55% students passed in Biology, 62% passed in Physics, 60% passed in Chemistry, 25% passed in Physics and Biology, 30% passed in Physics and Chemistry, 28% passed in Biology and Chemistry. Only 2% failed in all the subjects.If the number of students is 360, then how many passed in at least two subjects?

a) 265

b) 263

c) 270

d) 260

Question : 5

In a school there are 30 teachers who teach Mathematics or Physics. Of these teachers, 20 teach Mathematics and 15 teach Physics, 5 teach both Mathematics and Physics. The number of teachers teaching only Mathematics is

a) 15

b) 10

c) 5

d) 20

Question : 6

Which one of the following is not correct in respect of the sets A and B?

a) If A ⊆ B, then B ∩ A = A

b) If A ⊆ B, then A ∩ (A – B) = Φ

c) If A ⊆ B, then B ∪ A = B

d) If A ∩ B = Φ, then either A = Φ or B = Φ