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) A
B = {2, 3, 4, 5, 6, 7, 8}
(A
B)’ = {1, 9}
A’ = {1, 3, 5, 7, 9}
B’ = {1, 4, 6, 8, 9}
A’
B’ = {1, 9}
(A
B)’ = A’
B’
Hence proved
(ii) A
B = {2}
(A
B)’ = {1, 3, 4, 5, 6, 7, 8, 9}
A’
B’ = {1, 3, 4, 5, 6, 7, 8, 9}
(A
B)’ = A’UB’
Hence proved
These are also known as De Morgan’s theorem
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