Question

If $n(P)=8,n(Q)=10$ and $n(R)=5{(}^{\prime }{n}^{\prime }$ denotes cardinality) for three disjoint sets $P,Q,R$ then $n(P\cup Q\cup P)=$

• A. $23$
• B. $20$
• C. $18$
• D. $15$

Answer 1

Answer: (A)

We have, $n\left(P\right)=8$, $n\left(Q\right)=10$ and $n\left(R\right)=5$
Since $P,Q$ and $R$ are disjoint sets
$\therefore n\left(P\cap Q\right)=n\left(Q\cap R\right)=n\left(R\cap P\right)$
$=n\left(P\cap R\cap Q\right)=0$
Now, $n\left(P\cup Q\cup R\right)$
$=n\left(P\right)+n\left(Q\right)+n\left(R\right)$
$-n\left(P\cap Q\right)-n\left(Q\cap R\right)-n\left(R\cap P\right)+n\left(P\cap Q\cap R\right)$
$=8+10+5-0-0-0+0$
$=23$