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  4. If n(P) = 8,n(Q) = 10 and n(R) = 5 ('n' denotes cardinality) for three disjoint sets P, Q, R then n (P ∪ Q ∪ P ) =

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Q. 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 ) = $

J & K CETJ & K CET 2017Sets

Solution:

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