Question

Let $A$ and $B$ be subsets of $X$ and $C=(A\cap B^{\prime })\cup (A^{\prime }\cap B)$ where $A^{\prime }$ and $B^{\prime }$ are complements of $A$ and $B$ respectively in $X$. What is $C$ equal to?

• A. $(A\cap B^{\prime })-(A\cap B^{\prime })$
• B. $(A^{\prime }\cup B)-(A^{\prime }\cap B)$
• C. $(A\cup B)-(A\cap B)$
• D. $(A^{\prime }\cup B^{\prime })-(A^{\prime }\cap B^{\prime })$

Answer 1

The correct option is A $(A\cap B^{\prime })-(A\cap B^{\prime })$

Given : $C=(A\cap B^{\prime })\cup (A^{\prime }\cap B)$.

Hence, $C=(A\cup B)-(A\cap B)$