Question

If $n(P) = 8,n(Q) = 10$ and $n(R) = 5 ('n'$ 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)

$23$

Answer 2

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, $n\left(P\cup Q \cup R\right)$
$=n\left(P\right)+n\left(Q\right)+n\left(R\right)$
$-n\left(P\cap Q\right)-n\left(Q\cap R\right)-n \left(R\cap P\right)+n\left(P\cap Q\cap R\right)$
$=8+10+5-0-0-0+0$
$=23$