Choose the correct answers from the given four option: If $A = \{1, 3, 5, 7, 9, 11, 13, 15, 17\}$, $B = \{2,…

Choose the correct answers from the given four option: If $A = \{1, 3, 5, 7, 9, 11, 13, 15, 17\}$, $B = \{2, 4, \ldots, 18\}$ and $N$ the set of natural numbers is the universal set, then $A' \cup (A \cup B) \cup B'$ is.

  1. B

  2. A

  3. N

  4. \(\phi\)

Solution

Solution:

Given that:

A = {1, 3, 5, 7, 9, 11, 13, 15, 17}

B = {2, 4, ...., 18}

U = N = {1, 2, 3, 4, 5, .....}

\(\text{A}'\cup(\text{A}\cup\text{B})\cap\text{B}'=\text{A}'\big[(\text{A}\cap\text{B}')\cup(\text{B}\cap\text{B}')\big]\)

\(=\text{A}'\cup(\text{A}\cap\text{B}')\cup\phi \ \big[\because \text{A}\cap\text{A}'=\phi\big]\)

\(=\text{A}'\cup(\text{A}\cap\text{B}')\)

\(=(\text{ A}'\cup\text{A})\cap(\text{A}'\cup\text{B}')\)

\(=\text{N}\cup(\text{A}'\cup\text{B}')\ \big[\because \text{A}'\cup\text{A}=\text{N}\big]\)

\(=\text{A}'\cup\text{B}'\)

\(=(\text{A}\cup\text{B}')=(\phi)'=\text{N} \ \big[\because \text{A}\cap\text{B}=\phi\big]\)

Hence, the correct option is (b).

Asked in: NCERTEXAMPLER

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