Question

Sets A and B have 3 and 6 elements respectively. The minimum number of elements in $(A\cup B)$ is 6. State True/False.

• A. 3
• B. 6

Answer 1

The correct option is A

3

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)=3+6-1(A\cap B)$

Since maximum number of elements in $A\cap B=3$

$\therefore$ Minimum number of elements in $A\cup B=9-3=6$.