Question

If$n\left(A\right)=15,n\left(B\right)=20,n\left(A\cap B\right)=10$. find$n\left(A\cup B\right)$.

Short answer

$n\left(A\cup B\right)=25$.

Step-by-step solution

Step 1. Given Information.

The given values are

$n\left(A\right)=15,n\left(B\right)=20,n\left(A\cap B\right)=10$.

Step 2. Value of nA∪B.

Using the Counting principle, we get

$n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$

$$\begin{gathered} n\left(A\cup B\right)=15+20-10 \\ n\left(A\cup B\right)=25 \end{gathered}$$.