1.

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’)

Answer»

(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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