Choose the correct answers from the given four option: If X and Y are two sets and X′ denotes the complement…

Choose the correct answers from the given four option:

If X and Y are two sets and X′ denotes the complement of X, then \(\text{X}\cap(\text{X}\cup\text{Y})'\) is equal to.

  1. \(\text{X}\cap\text{Y}.\)

  2. \(\text{X}.\)

  3. \(\phi.\)

  4. \(\text{Y}.\)

Solution

Solution:

Let \(\text{x}\in\text{X}\cap(\text{X}\cup\text{Y})'\)

\(\Rightarrow \text{x}\in\text{X}\cap(\text{X}'\cup\text{Y})'\)

\(\Rightarrow \text{x}\in(\text{X}\cap\text{X})\cap(\text{X}\cap\text{Y}')\)

\(\Rightarrow \text{x}\in\phi\cap(\text{x}\cap\text{Y}')\ \big[\because \text{A}\cap\text{A}'=\phi\big]\)

\(\Rightarrow \text{x}\in\phi\)

Hence, the correct option is (c).

Asked in: NCERTEXAMPLER

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