If A and B are two sets, then A (A B) equals. - Vidyadip

MCQ

If $A$ and $B$ are two sets, then $\text{A} \cap (\text{A} \cup \text{B})$ equals.

✓
$\text{A}$
B
$\text{B}$
C
$\phi$
D
$\text{A}\cap\text{B}$

✓

Answer

Correct option: A.

$\text{A}$

Given that: $\text{A}\cap(\text{A}\cup\text{B})$
Let $\text{x}\in\text{A}\cap(\text{A}\cup\text{B})$
$\Rightarrow \text{x}\in\text{A}$ and $\text{x}\in(\text{A}\cup\text{B})$
$\Rightarrow \text{x}\in\text{A}$ and $(\text{x}\in\text{A}\text{ or x}\in\text{B})$
$\Rightarrow (\text{x}\in\text{A}$ and $\text{x}\in\text{A})$ or $(\text{x}\in\text{A}$ and $\text{x}\in\text{B})$
$\Rightarrow \text{x}\in\text{A}$ or $\text{x}\in(\text{A}\cap\text{B})$
$\Rightarrow \text{x}\in\text{A}$
Hence, the correct option is $(a).$

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