The set (A ')' is equal to: - Vidyadip

MCQ

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

A
$\text{A}'\cup\text{B}\cup\text{C}$
✓
$\text{A}'\cup\text{B}$
C
$\text{A}'\cup\text{C}'$
D
$\text{A}'\cap\text{B}.$

✓

Answer

Correct option: B.

$\text{A}'\cup\text{B}$

$\text{(A}\cup\text{B}')'\cup\text{(B}\cap\text{C})$
$=[\text{A}\cap\text{(B}')']\cup\text{(B}\cap\text{C})$ (De Morgen law)
$=\text{(A}'\cap\text{B})\cup\text{(B}\cap\text{C})$
$=\text{(A}'\cup\text{C})\cup\text{B}$ (Distributive law)
Disclimer: The question seems to be incorrect or there is some printing mistake in the question. The options given in the question does not match with the answer.

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