Question

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $A\cup B$

• A. 3
• B. 6
• C. 9
• D. 18

Answer 1

The correct option is B

6

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

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

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