Set Theory Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11

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 : 12

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 : 13

If A and B are any two non-empty subsets of a set E, then what is A ∪ (A ∩ B) equal to?

a) A

b) A ∪ B

c) A ∩ B

d) B

Question : 14

If a set A contains 60 elements and another set B contains 70 elements and there are 50 elements in common, then how many elements does A ∪ B contain?

a) 80

b) 100

c) 130

d) 70

Question : 15

Which one of the following is a null set?

a) C = {Φ}

b) B = {x : x + 3 = 3}

c) A = {x is a real number : x > 1 and x < 1}

d) D = {x is a real number : x ≥ 1 and x ≤ 1}