Q. 4

# If U = {1, 2, 3,

(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

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