If X and Y are two sets and X' represents the compliment of X then X⋂(X⋃Y)' is equal to
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X∩(Y∪X) ′
=X∩(Y ′ ∩X ′ ) . . ( De Morgan's laws)
= X∩Y ′ ∩X ′
=X∩X ′ ∩Y ′ . . ( their is no common part between X & X' o
= ϕ∩Y ′ =ϕ
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