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

Question : 1

Consider the following statements:
I. Set of points of a given line is a finite set.
II. Intelligent students in a class is a set.
III. Good books in a school library is a set.
Which of the above statements is/are not correct?

a) Both I and II

b) Both II and III

c) Only I

d) I, II and III

Question : 2

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.What is the ratio of number of students who passed in both Physics and Chemistry to number of students who passed in both Biology and Physics but not Chemistry?

a) 9 : 7

b) 10 : 7

c) 7 : 10

d) 7 : 9

Question : 3

Which one of the following is a correct statement?

a) {a, b} ⊆ {{a}, b, c}

b) {a} ⊆ {{a}, b, c}

c) {a} ε {{a}, {b}, c}

d) a ⊆ {{a}, b, c}

Question : 4

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

a) B

b) A

c) Φ

d) B'

Question : 5

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 : 6

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