UPSC NDA Math Model Paper 6

Given: A = {2, 4, 6, 8, 10}, B = {4, 8, 12, 16} and U = {2, 4, 6, 8, 10, 12, 14, 16, 18} where U is the universal set for A and B.
Here, we have to find the value of A' ∩ B'
As we know that, (A ∪ B)' = A' ∩ B'
⇒ A ∪ B = {2, 4, 6, 8, 10} ∪ {4, 8, 12, 16} = {2, 4, 6, 8, 10 ,12, 16}
As we know that, A' = U - A
⇒ (A ∪ B)' = U - (A ∪ B) = {2, 4, 6, 8, 10, 12, 14, 16, 18} - {2, 4, 6, 8, 10 ,12, 16} = {14, 18}