Question

If P and Q are two sets such that P has 40 elements, $P\cup Q$ has 60 elements and $P\cap Q$ has 10 elements, how many elements does Q have?

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ n\left(P\right)=40 \\ n\left(P\cup Q\right)=60 \\ n\left(P\cap Q\right)=10 \\ \mathrm{To}\mathrm{find}: \\ n\left(Q\right) \\ \mathrm{We}\mathrm{know}: \\ n\left(P\cup Q\right)=n\left(P\right)+n\left(Q\right)-n\left(P\cap Q\right) \\ \Rightarrow 60=40+n\left(Q\right)-10 \\ \Rightarrow n\left(Q\right)=30 \end{gathered}$$