Let A and B have 3 and 6 elements respectively. What can be the m… - Vidyadip

MCQ

Let 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

6

Solution:

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

Now A has 3 elements and B has 6 elements. If they are disjoint, then n(A ∩ B) = 0.

$\therefore$ n(A ∪ B) = 6 + 3 = 9

If A ⊂ B then A ∪ B = B

$\therefore$ (A ∪ B) = n(B) = 6

B cannot be a subset of A and hence the other possibility of A ∪ B = A is ruled out.

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