Question

If $X$ and $Y$ are two subsets of the universal set $U$ and $X^{\prime }$ denotes the complement of $X,$ then $X\cup {\left(X\cap Y\right)}^{\prime }$ is equal to

• A. $X$
• B. $Y^{\prime }$
• C. $\varphi$
• D. $U$

Answer 1

The correct option is D $U$

$X\cup (X\cap Y{)}^{\prime }=X\cup (X^{\prime }\cup Y^{\prime })$ (Using DeMorgans rule)

$=(X\cup X^{\prime })\cup (X\cup Y^{\prime })=U\cup (X\cup Y^{\prime })=U$