Question

If $A$ and $B$ are two sets, then $(AUB)\text{'}\cap (A\text{'}\cup B)$ is equal to

• A. $A\text{'}$
• B. $A$
• C. $B\text{'}$
• D. None of these

Answer 1

The correct option is A

$A\text{'}$

Explanation for the correct option:

Find the value of $(AUB)\text{'}\cap (A\text{'}\cap B)$:

By applying Distributive law, we get

$\begin{array}{rcl}& \Rightarrow & A\text{'}\cup \left[(B\text{'}\cap B)\right]=A\text{'}\cup \varphi \\ & =& \mathit{A}\mathbf{\text{'}}\end{array}$

Hence, Option ‘A’ is Correct.