Choose the correct answers from the given four option: The set (A… - Vidyadip

MCQ

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.

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.

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

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 $(b).$

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