Question

If set A and set B have 3 and 6 elements respectively, then which of the following 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

Given that n(A) = 3 and n(B) = 6.

If set A and set B have all distinct elements, then $A\cup B$ will have 9 elements.

$\Rightarrow$ $A\cup B$ will have a maximum of 9 elements.

But, if any element is repeated, then $A\cup B$ will have less than 9 elements.

If all the elements of A are present in B i.e., $A\subseteq B$, then $A\cup B$ will have 6 elements.

So, the minimum number of elements in $A\cup B$ is 6.