MCQ
The set $\text{(A}\cup\text{B}')'\cup\text{B}\cap\text{C}$ is equal to:
- A$\text{A}'\cup\text{B}\cup\text{C}$
- B$\text{A}'\cup\text{B}$
- C$\text{A}'\cup\text{C}'$
- D$\text{A}'\cap\text{B}.$
✓
Answer
- $\text{A}'\cup\text{B}.$
Solution:
$\text{(A}\cup\text{B}')'\cup\text{(B}\cap\text{C})$
$=[\text{A}\cap\text{(B}')']\cup\text{(B}\cap\text{C})$ (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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