Question

Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B)\cup (B-A)\cup (A\cap B)$ is equal to

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

Answer 1

The correct option is A $A\cup B$

$(A-B)\cup (B-A)\cup (A\cap B)$
Representing above set using Venn diagram as follows.

$\therefore$ By Venn diagram,
$(A-B)\cup (B-A)\cup (A\cap B)\equiv A\cup B$