Question:
Let $A$ and $B$ be two sets having 3 and 6 elements respectively. Write the minimum number of elements that $A \cup B$ can have.
Solution:
We know that $n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$n(A \cup B)$ is minimum when $n(A \cap B)$ is maximum
so, $n(A \cap B)=3$
Hence, $n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$=3+6-3$
$=6$