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 does Q have ?

Answer 1

$n\left(P\right)=40$

$n(P\cup Q)=60$

$n(P\cap Q)=10$

$n(P\cup Q)=n\left(P\right)+n\left(Q\right)-n(P\cap Q)$

$60=40+n\left(Q\right)-10$

$n\left(Q\right)=60-40+10$

$n\left(Q\right)=30$