Question

If$n\left(A\cap B\right)=10,n\left(B\right)=20,n\left(A\cup B\right)=50$, find$n\left(A\right)$.

Short answer

$n\left(A\right)=40$.

Step-by-step solution

Step 1. Given Information.

The given values are$n\left(A\cap B\right)=10,n\left(B\right)=20,n\left(A\cup B\right)=50$.

Step 2. Calculation of nA.

Using the Counting principle, we get

$\begin{array}{rcl}n\left(A\cup B\right)& =& n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)\\ 50& =& n\left(A\right)+20-10\\ 50& =& n\left(A\right)+10\\ n\left(A\right)& =& 40\end{array}$.