Question

If n(A X B) = n(B X A) = 36 then which of the following may hold true?

(a) n(A)=2, n(B)=18

(b) n(A)=9, n(B)=4

(c) n(A)=6, n(b)=6

(d) None of the mentioned

This question was posed to me in an interview.

This is a very interesting question from Cartesian Product of Sets topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

The correct option is (c) n(A)=6, n(b)=6

Explanation: n(A) should be equal to n(B) for n(A X B) = n(B x A).