If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, and = {2, 3, 5, 7} verify that:

(i) (A ∪ B)’ = (A’ ∩ B’)

(ii) (A ∩ C)’ = (A’ ∪ B’)

(i) AB = {2, 3, 4, 5, 6, 7, 8}

(AB)’ = {1, 9}

A’ = {1, 3, 5, 7, 9}

B’ = {1, 4, 6, 8, 9}

A’B’ = {1, 9}

(AB)’ = A’B’

Hence proved

(ii) AB = {2}

(AB)’ = {1, 3, 4, 5, 6, 7, 8, 9}

A’B’ = {1, 3, 4, 5, 6, 7, 8, 9}

(AB)’ = A’UB’

Hence proved

These are also known as De Morgan’s theorem