Question

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

• A. 3
• B. 6
• C. 9
• D. 18

Answer 1

Answer: (B)

6

Answer 2

n(A ∪ B) = n(1) + n(2) – n(A ∩ B) = $3 + 6 - n ( A \cap B )$

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

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