Question
If A and B are two sets, then $\text{A} \cap (\text{A} \cup \text{B})$ equals.
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$\text{A}$
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$\text{B}$
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$\phi$
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$\text{A}\cap\text{B}$
If A and B are two sets, then $\text{A} \cap (\text{A} \cup \text{B})$ equals.
$\text{A}$
$\text{B}$
$\phi$
$\text{A}\cap\text{B}$
Solution:
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 $(\text{x}\in\text{A}\text{ or x}\in\text{B})$
$\Rightarrow (\text{x}\in\text{A and x}\in\text{A})$ or $(\text{x}\in\text{A and x}\in\text{B})$
$\Rightarrow \text{x}\in\text{A}$ 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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