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in Sets, Relations and Functions by (48.8k points)
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If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to 

A. X

B. Y 

C. ϕ 

D. X ∩ Y

1 Answer

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Best answer

C. Φ

Given: X and Y are two sets

To find: X ∩ (X ∪ Y)′

X ∩ (X ∪ Y)′

{∵ A’ ∪ B’ = (A ∩ B)’}

= X ∩ (X’ ∩ Y′)

= (X ∩ X’) ∩ (X ∩ Y’)

= Φ ∩ (X ∩ Y’)

{∵ A’ ∩ A = Φ}

= Φ

{∵ Φ ∩ A = Φ}

Hence, X  (X  Y)′= Φ

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