If X and Y are two sets and $X^{'}$ denotes the complement of X, then find the value of $X \cap (X \cup Y)^{'}$ .

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Solution

$X \cap (X \cup Y)^{'} = X \cap (X^{'} \cap Y^{'}) [∵ (A \cup B)^{'} = A^{'} \cap B^{'}] = ({X \cap X}^{'}) \cap Y^{'} = ϕ \cap Y^{'} = ϕ [∵ ϕ \cap A = ϕ]$

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