Question

If$n\left(A\right)=8,n\left(B\right)=12,$and$n\left(A\cap B\right)=3,$find$n\left(A\cup B\right).$

Short answer

The final answer is $17$.

Step-by-step solution

Step 1. Given information.

The given information is -

$$\begin{gathered} n\left(A\right)=8 \\ n\left(B\right)=12 \\ n\left(A\cap B\right)=3 \end{gathered}$$

Step 2. Find nA∪B.

To find we apply the theorem of counting formula.

$$\begin{gathered} n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ =8+12-3 \\ =20-3 \\ =17 \end{gathered}$$