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