Question

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A U B )

• A. 3
• B. 6
• C. 9
• D. 18

Answer 1

The correct option is B

6

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

n(A $\cup$ B) will be minimum if n$(A\cap B)$ is maximum.
Since maximum number of elements in A $\cap$ B = 3
$\therefore$ Minimum number of elements in $A\cup B$ = 9 - 3 = 6 .