Choose the correct answers from the given four option: If A and B are two sets, then \(\text{A} \cap…

Choose the correct answers from the given four option:

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

  1. \(\phi\)

  2. \(\text{A}\cap\text{B}\)

  3. \(\text{B}\)

  4. \(\text{A}\)

Solution

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).

Asked in: NCERTEXAMPLER

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