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Question
The set (A ∩ B′)′ ∪ (B ∩ C) is equal to ______.
Options
A′ ∪ B ∪ C
A′ ∪ B
A′ ∪ C′
A′ ∩ B
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Solution
The set (A ∩ B′)′ ∪ (B ∩ C) is equal to A′ ∪ B.
Explanation:
We know that,
(A ∩ B)' = A' ∪ B'
∴ (A ∩ B')' ∪ (B ∩ C) = [A' ∪ (B')'] ∪ (B ∩ C)
= (A' ∪ B) ∪ (B ∩ C) ......[∵ (B')' = B]
= A' ∪ B
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