NCERT Solutions
Class 11 Maths
Sets

Ex.1.5 Q.4
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that
(1) (A ∪ B) ′ = A′ ∩ B′
(2) (A ∩ B) ′ = A′ ∪ B′
Given, U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}
(1) A ∪ B = {2, 3, 4, 5, 6, 7, 8}
(A ∪ B) ′ = = U - (A ∪ B) = {1, 9}
A’ = U – A = {1, 3, 5, 7, 9}
B’ = U – B = {1, 4, 6, 8, 9}
A’ ∩ B′ = {1, 9}
So, (A ∪ B) ′ = A′ ∩ B′ = {1, 9}
(2) A ∩ B = {2}
(A ∩ B)’ = U – (A ∩ B) = {1, 3, 4, 5, 6, 7, 8, 9}
A’ = U – A = {1, 3, 5, 7, 9}
B’ = U – B = {1, 4, 6, 8, 9}
A’ U B′ = {1, 3, 5, 7, 9} U {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9}
So, (A ∩ B) ′ = A′ ∪ B′