Question

For any two sets A and B, $\left\{\right(A\setminus B)\cup (B\setminus A\left)\right\}\cap (A\cap B)$ is:

• A. $\varphi$
• B. $A\cup B$
• C. $A\cap B$
• D. $A^{\prime }\cap B^{\prime }$

Answer 1

The correct option is A $\varphi$

$(A$ \ $B)\cup (B$ \ $A)$ contains that elements form set $A$ and $B$ that are not contained in the other set.

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

$\therefore (A$ \ $B)\cup (B$ \ $A)$ does not contain elements of $A\cap B$

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