If A and B are two sets such than n(A) = 54, n(B) = 39 and n(B – A) = 13 then find n(A ∪ B).

Hint n(B) = n(B – A) + n(A ∩ B) ⇒ n(A ∩ B) = (39 – 13) = 26.

Given: n(A) = 54, n(B) = 39, n(B – A) = 13

Using the hint

n(B) = n(B – A) + n(A ∩ B)

⇒ 39 = 13 + n(A ∩ B)

⇒ n(A ∩ B) = 39 – 13

⇒ n(A ∩ B) = 26

Visualizing the hint given,

We know that n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

⇒ n(A ∪ B) = 54 + 39 – 26

⇒ n(A ∪ B) = 67

Hence n(A ∪ B) = 67