Question

If in sets A, B, C, the set B ∩ C consists of 8 elements, set A ∩ B consists of 7 elements and set C ∩ A consists of 7 elements then the minimum element in set  A U B U C will be?

(a) 8

(b) 14

(c) 22

(d) 15

I got this question in an international level competition.

Question is from Algebraic Laws on Sets topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Right choice is (a) 8

The best I can explain: For minimum elements set B and C  have 8 elements each and all of the elements are same,  Also set A should have 7 elements which are already present in B and C. Thus A U B U C ≡ A ≡ B.