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Question
If X and Y are two sets and A′ denotes the complement of A, then X ∩ (X ∪ Y)′ is equal to
If X and Y are two sets and A′ denotes the complement of A, then X ∩ (X ∪ Y)′ is equal to
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Solution
The correct option is C ϕ
(X ∪ Y) is a collection of all the elements of set X and set Y.
(X ∪ Y)′ = X' ∩ Y' (By De Morgan's Law) or is a collection of all elements which are not in X and not in Y.
(X ∪ Y)′ has no element common with set X.
Hence X ∩ (X ∪ Y)′ is a null set.
(X ∪ Y) is a collection of all the elements of set X and set Y.
(X ∪ Y)′ = X' ∩ Y' (By De Morgan's Law) or is a collection of all elements which are not in X and not in Y.
(X ∪ Y)′ has no element common with set X.
Hence X ∩ (X ∪ Y)′ is a null set.