First slide

Operations on Sets

Question

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

Easy

A

3
B

6
C

9
D

18

Solution

$n (A \cup B) = n (A) + n (B) - n (A \cap B) = 3 + 6 - n (A \cap B)$
Since, maximum number of elements in $A \cap B = 3$
$∴$ Minimum number of elements in $A \cup B = 9 - 3 = 6 .$

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