Question

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

Answer 1

We know that

Case 1:- From (1), it is clear that $n(A\cup B)$ wiill be maximum when $n(A\cap B)=0$

In that case, $n(A\cup B)=n\left(A\right)+n\left(B\right)=(3+6)=9$

$\therefore$ maximum number of elements in $A\cup B=9$

Case 2:- From (1), it is clear that $n(A\cup B)$ wiill be maximum when $n(A\cap B)$ is maximum, i.e., when $n(A\cap B)=3$

In this case, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)=(3+6-3)=6$

$\therefore$ maximum number of elements in $A\cup B=6$