Question

Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Then A’∩B’ is equal to (A∪B)’.

(a) True

(b) False

I have been asked this question during an interview.

This intriguing question originated from Complement of a Set topic in portion Sets of Mathematics – Class 11

Answer 1

The correct answer is (a) True

Easiest explanation: Complement of a set A is a set which contains elements of U which are not the elements of A. A’ = U-A = {1, 2, 3, 4, 5, 6} – {1,4} = {2,3,5,6} and B’ = U-B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}. A’∩B’= {2,3,5,6} ∩ {1,4,6} = {6}.

A∪B = {1,2,3,4,5} => (A∪B)’={6}.

Hence, A’∩B’=(A∪B)’.