# MCQ Set Theory

Collection of Multiple choice questions and Answers (MCQs) focuses on “Set Theory” along with their solution and justification.

Let and , then which of the following statements is correct?
(A) in (B) with respect to (C) with respect to (D) with respect to We have, in The set of elements in which are not in  in is false, because is not an element of in  in is false, because is not an element of in  in is correct, because the only element of namely also belongs to in . in is false, because is not a set.

If , , and then is
(A) 9
(B) 8
(C) 6
(D) None of these

Explanation:
We have, Now,   Two finite sets have and elements, then total number of subsets of the first set is 56 more that the total number of subsets of the second. The values of and are,
(A) 7, 6
(B) 6, 3
(D) 5, 1
(D) 8, 7

Solution: (B)
Since the two finite sets have and elements, so number of subsets of these sets will be and respectively. According to the question putting , , we get or If A has 3 elements and B has 6 elements, then the minimum number of elements in the set is
(A) 6
(B) 3
(C) (D) None of these

Clearly the number of elements in will be minimum when . Hence the minimum number of elements in is the same as the number of elements in B, that is, 6.
Clearly the number of elements in will be minimum when . Hence the minimum number of elements in is the same as the number of elements in