Question

If$n\left(A\right)=12,n\left(A\cup B\right)=30,$and$n\left(A\cap B\right)=6$, find$n\left(B\right).$

Short answer

The final answer is$24.$

Step-by-step solution

Step 1. Given information.

$$\begin{gathered} n\left(A\right)=12 \\ n\left(A\cup B\right)=30 \\ n\left(A\cap B\right)=6 \end{gathered}$$

Step 2. Find nB.

To find we apply the counting formula.

That is,

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

So,

$$\begin{gathered} n\left(B\right)=n(A\cup B)+n\left(A\cap B\right)-n\left(A\right) \\ =30+6-12 \\ =36-12 \\ =24 \end{gathered}$$

Thus n(B) =$24.$