Question

If A and B are two sets containing 3 and 6 elements respectively, what can be the minimum number of elements in $A\cup B$ ? Also find minimum number of elements in $A\cap B$ ?

Answer 1

Minimum no. of elements in $A\cup B$

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)=3+6-3=6$
$n_{min}(A\cap B)=0$ [no intersection]