Chapter 13, Problem 3RE

To determine

To find: $n\left(B\right)$

Answer to Problem 3RE

$n\left(B\right) = 24$

Explanation of Solution

Given:

If $n\left(A\right) = 12$, $n\left(A{{\displaystyle \cap }}^{\text{}}B\right) = 6$ and $n\left(A{{\displaystyle \cup }}^{\text{}}B\right) = 30$.

Formula used:

$n\left(A{{\displaystyle \cup }}^{\text{}}B\right) = n\left(A\right) + n\left(B\right) - n\left(A{{\displaystyle \cap }}^{\text{}}B\right)$

Calculation:

$n\left(A\right) = 12$, $n\left(A{{\displaystyle \cap }}^{\text{}}B\right) = 6$ and $n\left(A{{\displaystyle \cup }}^{\text{}}B\right) = 30$

$n\left(A{{\displaystyle \cup }}^{\text{}}B\right) = n\left(A\right) + n\left(B\right) - n\left(A{{\displaystyle \cap }}^{\text{}}B\right)$

$30 = 12 + n\left(B\right) - 6$

$n\left(B\right) = 24$