Question

For two sets $A$ and $B$, $(A\cup B)\cap (A^{\prime }\cup B^{\prime })=$

• A. $A\cap B$
• B. $A\cup B$
• C. $A-B$
• D. $A\Delta B$

Answer 1

The correct option is D $A\Delta B$

$(A\cup B)\cap (A^{\prime }\cup B^{\prime })$
$=(A\cup B)\cap [U-(A\cap B\left)\right]$
$=(A\cup B)-(A\cup B)\cap (A\cap B)$
$=(A\cup B)-(A\cap B)=A\Delta B$