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

Question : 1

A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A ?

a) Two

b) One

c) No integer

d) Three

Question : 2

Which one of the following is a correct statement?

a) Φ = P(Φ)

b) Φ ∉ P (Φ)

c) Φ ε Φ

d) Φ ε P(Φ)

Question : 3

Which one of the following is an infinite set?

a) {x : x is a positive integer less than or equal to 1000}

b) {x : x is a natural number less than 1000}

c) {x : x is a whole number less than or equal to 1000}

d) {x : x is an integer and less than 1000}

Question : 4

The set of natural numbers is closed under
I. addition
II. subtraction
III. multiplication
IV. division
Which of the above is/are correct?

a) I, II and III

b) Both I and III

c) Only I

d) Both III and IV

Question : 5

The Venn diagram given above represents four sets of students who have opted for Mathematics, Physics, Chemistry and Electronics. What does the shaded region represent?

a) Students who opted for Mathematics, Physics and Electronics only

b) Students who opted for Mathematics, Physics and Chemistry

c) Students who opted for Physics, Chemistry and Electronics

d) Students who opted for Mathematics, Chemistry and Electronics only

Question : 6

Let x ε {2, 3, 4} and y ε {4, 6, 9, 10}. If A be the set of all order pairs (x, y) such that x is a factor of y. Then, how many elements does the set A contain?

a) 7

b) 10

c) 12

d) 6