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in Sets, Relations and Functions by (46.3k points)
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If A, B and C are three finite sets, then what is [(A ∪ B) ∩ C]′ equal to ?

(a) (A′ ∪ B′) ∩ C′ 

(b) A′∩ (B′ ∩ C′) 

(c) (A′ ∩ B′) ∪ C′ 

(d) (A ∩ B) ∩ C

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Best answer

(c) (A′ ∪ B′) ∪ C′

Given, A, B and C are three finite sets, then 

[ (A ∪ B) ∩ C ]′ = (A ∪ B)′ ∪ C′ 

= (A′ ∪ B′) ∪ C′

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