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

Question : 1

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 : 2

Let S be a set of first ten natural numbers. What is the possible number of pairs (a, b) where a, b E S and a ≠ b such that the product ab (> 12) leaves remainder 4 when divided by 12 ?

a) 8

b) 6

c) 4

d) 10

Question : 3

If two sets A and B have 2n and 4n elements, respectively. When n is a natural number. What can be the minimum number of elements in A ∪ B?

a) 4n

b) 3n

c) 2n

d) 6n

Question : 4

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 : 5

Consider the following in respect of the sets A and B.
I. (A ∩ B) ⊆ A
II. (A ∩ B) ⊆ B
III. A ⊆ (A ∪ B)
Which of the above are correct?

a) I and III

b) II and III

c) I and II

d) I, II and III

Question : 6

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