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

Question : 1

Let A = {7, 8, 9, 10, 11, 12} and B = {7, 10, 14, 15}. What is the number of elements in (A–B) and (B–A) respectively ?

a) 2 and 2

b) 4 and 2

c) 2 and 4

d) 4 and 4

Question : 2

In an examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% candidates failed in both English and Mathematics, what percentage of candidates passed in both the subjects?

a) 23%

b) 21%

c) 18%

d) 25%

Question : 3

Let A and B be finite non-empty sets with the number of elements in A = m and number of elements in B = n. Let m > n. If for some integer k ≥ 1, the number of nonempty subsets of A = $2^k$ + the number of non-empty subsets of B, then which one of the following is correct?

a) m = n + p for some odd prime number p

b) m = n + 1

c) m = n + 2

d) m = n + t for some composite number t

Question : 4

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}

Question : 5

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 : 6

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