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

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

(A) B ∩ C′ 

(B) A ∩ C 

(C) B ∪ C′ 

(D) A ∩ C′

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1 Answer

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Best answer

The correct choice is (A).

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