Question

If $A$ and $B$ are two sets, then $A\cap (A\cup B)$ is equal to

• A. $A$
• B. $B$
• C. $\varphi$
• D. None of these

Answer 1

The correct option is A

$A$

Explanation for the correct option:

Find the value of $\mathit{A}\mathbf{}\mathbf{\cap }\mathbf{}\mathbf{(}\mathit{A}\mathbf{}\mathbf{\cup }\mathbf{}\mathit{B}\mathbf{)}$:

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

$\Rightarrow x\in A$and $x\in (A\cup B)$

$\Rightarrow x\in A$and $(x\in Aorx\in B)$

$\Rightarrow (x\in A$and $x\in A)$or $(x\in A$and $x\in B)$

$\Rightarrow x\in A$or $x\in A\cap B$

$\Rightarrow x\in A$

$\mathbf{\therefore }A\cap (A\cup B)=A$

Hence, Option ‘A’ is Correct.