UPSC NDA Math Model Paper 6

Given: sets A and B has 4 and 8 elements respectively
⇒ n (A) = 4 and n (B) = 8
As we know that, n (A ∪ B) = n (A) + n (B) - n (A ∩ B)
⇒ n (A ∪ B) = 4 + 8 - n (A ∩ B)
Now in order to maximize n (A ∪ B) we have to minimize n (A ∩ B).
So, if A and B are disjoint i.e A ∩ B is an empty set, then n (A ∩ B) = 0.
⇒ n (A ∪ B) = 4 + 8 - 0 = 12
So, the maximum value of n (A ∪ B) = 12.