Question

Let $A$ and $B$ be two sets, then $(A\cup B^{\prime })\cap (A^{\prime }\cap B)$ is equal to

• A. $A^{\prime }$
• B. $A$
• C. $B^{\prime }$
• D. None of these

Answer 1

The correct option is D None of these

$=(A\cup B^{\prime })\cap (A^{\prime }\cap B)$

$=(A\cup B^{\prime })\cap {(A\cup B^{\prime })}^{\prime }$ (by De Morgan's Law)

$=X\cap X^{\prime }$ where $X=A\cup B^{\prime }$

$=\varphi$