Sets A and B have 3 and 6 elements respectively. What can be the minimum and maximum number of elements in
(i)A ∩ B (ii)A ∪ B
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)minimum n(A ∩ B) = 0, maximum n(A ∩ B) = 3
(ii)minimum n(A ∪ B) = 6, maximum n(A ∪ B) = 9
Sol. 
for minimum n(A ∪ B), the set A is subset of B and for maximum n(A ∪ B), the sets A and B are disjoint set.
also n(A ∪ B) = n(a) + n(b) – n(A ∩ B)
⇒ minimum n(A ∩ B) = 0, maximum n(A ∩ B) = 3
⇒ minimum value of n(A ∪ B) = 3 + 6 – 3 = 6 or maximum value of n(A ∪ B) = 3 + 6 – 0 = 9
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