Question

If $n\left(A\right)=8$ and $n(A\cap B)=2$, then $n\left[(A\cap B\text{'})\cap A\right]$ is equal to

• A. $2$
• B. $4$
• C. $6$
• D. $8$
• E. $10$

Answer 1

The correct option is C

$6$

Explanation for the correct option

Given: $n\left(A\right)=8$ and $n(A\cap B)=2$.

We know that $(A\cap B\text{'})\cap A$ can be written as $A-\left(A\cap B\right)$

Thus,

$\begin{array}{rcl}n\left[(A\cap B\text{'})\cap A\right]& =& n\left(A\right)-n\left(A\cap B\right)\\ & =& 8-2\\ & =& 6\end{array}$

Hence, option(C) i.e. $6$ is the correct option.