Question

It A = {1,2,3,4}, B = {3,4,5,6} , C = {2,4,6}
Then show that AU(BUC) = (AUB) U (AUC)
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Answer 1

BUC = {3,4,5,6} U {2,4,6}

= {2,3,4,5,6}

AUB = {1,2,3,4} U {3,4,5,6}

= {1,2,3,4,5,6}

AUC = {1,2,3,4} U {2,4,6}

= {1,2,3,4,6}

AU(BUC) = {1,2,3,4} U {2,3,4,5,6}

= {1,2,3,4,5,6}

(AUB) U (AUC) = {1,2,3,4,5,6} U {1,2,3,4,6}

= {1,2,3,4,5,6}

{1,2,3,4,5,6} = {1,2,3,4,5,6}

Therefore,

AU(BUC) = (AUB) U (AUC)

Hope it helps

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