For two sets A and B , if n(A) = 7, n(B) = 13 and n(A B) = 5 , then...

$∵ n\left(A\right) = 7, n\left(B\right) = 13$
$∵ \text{n}\left(\text{A} - \text{B}\right) = \text{n}\left(\text{A}\right) - \text{n}\left(\text{A} \cap \text{B}\right) = 7 - 5 = 2$
$n \left(A \cup B\right) = n \left(A\right) +$n\left(B\right)$-$n\left(A \cap B\right)$<br />$= 7 + 13 - 5 = 15$<br />$n \left(A \timesB\right) = n \left(A\right)\timesn \left(B\right)$<br />$7 \times13 = 91$<br />$\text{n} \left\{\left(\text{A}\cup \text{B}\right) \times \left(\text{A}\cap \text{B}\right)\right\}$= 15$\times5 = 75