Question

For any two non-empty sets $A$ and $B$, $(A\cup B{)}^C\cap (A^C\cap B)$ is equal to

• A. $A^C$
• B. $B^C$
• C. $\varphi$
• D. $A\cup B$

Answer 1

The correct option is C $\varphi$

As we know that
$(P\cup Q{)}^C=P^C\cap Q^C$
So, $(A\cup B{)}^C\cap (A^C\cap B)$
$=A^C\cap B^C\cap (B\cap A^C)=A^C\cap ((B^C\cap B)\cap A^C)=A^C\cap (\varphi \cap A^C)=A^C\cap \varphi =\varphi$