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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

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
 

Answers (1)

The answer is option (c)

Let 

        \begin{aligned} x \in X\cap (X\cup Y)' \\ x\in X\cap (X'\cap Y') \\ x\in (X\cap X')\cap (X\cap Y')\\x\ x\in \phi \cap (X\cap Y')\\x\in\phi\end{aligned}

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infoexpert22

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