Question

If $A$ and $B$ are two sets such that $A$ has $50$ elements, $B$ has $65$ elements and $A\cup B$ has $100$ elements, how many elements does $A\cap B$ have?

Answer 1

$n\left(A\right)=50$

$n\left(B\right)=65$

$n(A\cup B)=100$

$n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$=50+65-100$

$=115-60$

$n(A\cap B)=15$