Aspire Faculty ID #13833 · Topic: JAMIA MILLIA ISLAMIA MCA 2021 · Just now
JAMIA MILLIA ISLAMIA MCA 2021

$\text{The set }(A\cap B)'\ \cup\ (B\cap C)\ \text{ is equal to:},$

Solution

$ (A\cap B)'=A'\cup B' ,$ (De Morgan) $\Rightarrow (A\cap B)'\cup(B\cap C)=(A'\cup B')\cup(B\cap C)=A'\cup\big(B'\cup(B\cap C)\big)$ $B'\cup(B\cap C)=(B'\cup B)\cap(B'\cup C)=U\cap(B'\cup C)=B'\cup C$ $\Rightarrow A'\cup(B'\cup C)=A'\cup B'\cup C$
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