Question

If X and Y are two sets then $X\cap (Y\cup X{)}^{\prime }$ equals:

• A. $X$
• B. $Y$
• C. $\varphi$
• D. $\left\{0\right\}$

Answer 1

Answer: (C)

$\varphi$

We have $X\cap {(Y\cup X)}^{\prime }=X\cap (Y^{\prime }\cap X^{\prime })$
= $X\cap Y^{\prime }\cap X^{\prime }=X\cap X^{\prime }\cap Y^{\prime }$
= $\varphi \cap Y^{\prime }=\varphi$