Question

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

• A. $37$
• B. $38$
• C. $45$
• D. $52$

Answer 1

The correct option is D $52$

$n\left(U\right)=60\left(UniversalSet\right)$

$n(P\cap Q)=5$

$n(Q\cap R)=10$

$n\left(P\right)=20$

$n\left(Q\right)=23$

$n(P\cup Q)=n\left(P\right)+n\left(Q\right)-n(P\cap Q)=20+23-5=38$

$n\left(R\right)=n\left(U\right)-n(P\cup Q)+n(Q\cap R)=60-38+10=32$

$n(P\cup R)=n\left(P\right)+n\left(R\right)-n(P\cap R)=20+32-0=52$