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  • The set (A ∩ B′)′ ∪ (B ∩ C) is equal to A. A′∪ B ∪ C B. A′ ∪ B C. A′ ∪ C′ D. A′ ∩ B

The set (A ∩ B′)′ ∪ (B ∩ C) is equal to
A. A′∪ B ∪ C
B. A′ ∪ B
C. A′ ∪ C′
D. A′ ∩ B
 

Answers (1)

The answer is option B.

We know that 

            \begin{aligned} (A\cap B)' &= A'\cup B' &\quad& [\text{De Morgan's Law}] \\ (A\cap B)'\cup (B\cap C) &= \left[A'\cup B' \right ]\cup(B\cap C)\\ & =(A'\cup B)\cup (B\cap C) && [(B')' = B] \\ &= A'\cup B\end{aligned}

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infoexpert22

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