Single Choice

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

A$$37$$
B$$38$$
C$$45$$
D$$52$$
Correct Answer

Solution

$$n(U) =60 (Universal \; Set) $$

$$n(P \cap Q ) = 5$$

$$n(Q \cap R ) = 10$$

$$n(P ) = 20$$

$$n(Q)=23$$

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

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

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

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