Question

If $A$ and $B$ are two given sets, then $A\cap (A\cap B{)}^c$ is equal to

• A. $A$
• B. $B$
• C. $\varphi$
• D. $A\cap B^c$

Answer 1

The correct option is D $A\cap B^c$

$A\cap (A\cap B{)}^c$

$=A\cap (A^c\cup B^c)$ (De Morgan's Law)

$=(A\cap A^c)\cup (A\cap B^c)$

$=\varphi \cup (A\cap \varphi B^c)$

$\therefore A\cap (A\cap B{)}^c=A\cap B^c$