Question

If X and Y are two sets and $X^{\prime }$ denotes the complement of X, then
$X\cap (X\cup Y{)}^{\prime }$ is equal to

• A. X
• B. Y
• C. $\varphi$
• D. $X\cap Y$

Answer 1

The correct option is C

$\varphi$

$X\cap (X\cup Y{)}^{\prime }=X\cap (X^{\prime }\cap Y^{\prime }\left)\right[\because (A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }]=\left({X\cap X}^{\prime }\right)\cap Y^{\prime }=\varphi \cap Y^{\prime }=\varphi [\because \varphi \cap A=\varphi ]$