Q43 of 58 Page 12

If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to

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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