Question

If$n\left(A\cap B\right)=40,n\left(B\right)=n\left(A\right),n\left(A\cup B\right)=60$. Find$n\left(A\right)$.

Short answer

$n\left(A\right)=50$.

Step-by-step solution

Step 1. Given Information.

The given values are

$n\left(A\cap B\right)=40,n\left(B\right)=n\left(A\right),n\left(A\cup B\right)=60$.

Step 2. Calculation of nA.

Using the Counting principle, we get

$\begin{array}{rcl}n\left(A\cup B\right)& =& n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)\\ 60& =& 2n\left(A\right)-40\\ 100& =& 2n\left(A\right)\\ n\left(A\right)& =& 50\end{array}$.