The universal set of U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}, B = {3, 5, 6} then determine (A′ ∩ B′).

Question: The universal set of U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}, B = {3, 5, 6} then determine (A′ ∩ B′).

Solution:
Given,
U = {1, 2, 3, 4, 5, 6}
A = {1, 3, 5}
B = {3, 5, 6}

A‘ = U - A
= {1, 2, 3, 4, 5, 6} - {1, 3, 5}
= {2, 4, 6}

B‘ = U - B
= {1, 2, 3, 4, 5, 6} - {3, 5, 6}
= {1, 2, 4}

Now
(A‘ ∩ B‘) = {2, 4, 6} ∩ {1, 2, 4}
= {2, 4}