Question

P, Q and R are three sets and $\xi P\cup Q\cup R.$Given that n$\left(\xi \right)$ = 60, $n(P\cap Q)=5$, n(Q $\cap R$) = 10, n(p) = 20$and$n(Q) = 23,$find$n (P' $\cup Q$)

• A. 37
• B. 38
• C. 45
• D. 52

Answer 1

The correct option is C 45

$n\left(Q\right)-n(P\cap Q)-n(Q\cap R)=23-5-10=8$

$8+n\left(P\right)+n\left(R\right)=60$

$n\left(R\right)=60-8-20=32$

$n(P^{\prime }\cup Q)=n\left(R\right)+n\left(Q\right)-n(Q\cap R)$

$=32+23-10=45$