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Idea of a Set

If X and ...

Question

If $X$ and $Y$ are two sets, $X \cap {(Y \cup X)}^{C}$ is equal to

A

X

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B

Y

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C

ϕ

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D

X \cap Y

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Solution

The correct option is C $ϕ$
$X \cap (Y \cup X)^{C} = X \cap (Y^{C} \cap X^{C})$
$= (X \cap Y^{C}) \cap (X \cap X^{C})$
$= (X \cap Y^{C}) \cap ϕ$
$= ϕ$

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