Question

Ifu={1,2,3,4,5,6,7,8,9}, A={2,4,6,8,}, and B= {2,3,5,7}
verify that (a) (AUB)'=A'B'(a)(AB)'=A'U B

Answer 1

Step-by-step explanation:

U= {1,2,3,4,5,6,7,8,9}

A={2,4,6,8}

B= {2,3,5,7}

A'= {1,3,5,7,9}

B'= {1,4,6,8,9}

i) A'∩B' = {1,9}

AUB= {2,3,4,5,6,7,8}

(AUB)'= {1,9}

Hence, (AUB)'=A'∩B'

ii) A∩B = {2}

(A∩B)'={1,3,4,5,6,7,8,9}

A'UB' = {1,3,4,5,6,7,8,9}

Hence, (A∩B)' = A'UB'

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