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+1 vote
10.9k views
in Sets, Relations and Functions by (48.8k points)
reopened by

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

+1 vote
by (47.3k points)

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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