Question

If A and B are two sets, then
$(A\cup B)=(A-B)\cup (B-A)\cup (A\cap B)$

• A. True
• B. False

Answer 1

The correct option is A True

Let $x\in (A-B)\cup (B-A)\cup (A\cap B)$

$\Rightarrow (x\in (A-B)\text{or}x\in (B-A\left)\right)\text{or}(x\in (A\cap B\left)\right)$

$\Rightarrow (x\in A\text{and}x\notin B)\text{or}(x\in B\text{and}x\notin A)\text{or}(x\in A\text{and}x\in B)$

$\Rightarrow$$x\in A\text{or}x\in B$

$\Rightarrow (A\cup B)$

Hence True