Choose the correct answers from the given four option: The set \((\text{A} \cap \text{B}')' \cup (\text{B}…

Choose the correct answers from the given four option:

The set \((\text{A} \cap \text{B}')' \cup (\text{B} \cap \text{C})\) is equal to.

  1. \(\text{A}'\cup\text{C}'\)

  2. \(\text{A}'\cup\text{B}\cup\text{C}\)

  3. \(\text{A}'\cap\text{B}\)

  4. \(\text{A}'\cup\text{B}\)

Solution

Solution:

We konw that: \((\text{A}\cap\text{B})'=\text{A}'\cup\text{B}'\) [De Morgan's law]

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

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

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

Hence, the correct optiom is (b).

Asked in: NCERTEXAMPLER

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