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For all sets A and B, A ∪ (B – A) = A ∪ B
 

Answers (1)

\begin{aligned} A\cup (B-A)& = A\cup (B\cap A')\\ &=(A\cup B)\cap (A\cup A') &[\text{Distributive law}]\\ &=(A\cup B)\cap U&[A\cup A' = U] \\ &=A\cup B = RHS\end{aligned}

Hence the given statement is true.

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infoexpert22

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