Question

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

• A. $A$
• B. $B$
• C. $\varphi$
• D. None of these

Answer 1

Answer: (C)

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