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Question
The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′ is equal to ______.
Options
B ∩ C′
A ∩ C
B ∪ C′
A ∩ C′
Solution
The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′ is equal to B ∩ C′.
Explanation:
Since (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′
= (A ∪ (B ∪ C)) ∩ (A′ ∪ (B ∪ C)) ∩ C
= (A ∩ A′) ∪ (B ∪ C) ∩ C′
= Φ ∪ (B ∪ C) ∩ C′
= B ∩ C′ ∪ Φ
= B ∩ C′
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