If sets A and B have $3$ and $6$ elements each, then the minimum number of elements in $A \cup B$ is

3

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6

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9

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18

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Solution

The correct option is A $6$
$n (A) = 3; n (B) = 6$
Since minimum number of elements in $A \cup B$ is asked,
$\Rightarrow n (A \cap B) = 3$
$\Rightarrow n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$= 3 + 6 - 3$
$= 6$

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