Question

Let A and B be two sets such that n(A) = 45, n(B) = 38 and n(A ∪B) = 70, find: n(B – A)

Answer 1

n(A) = 45, n(B) = 38 and n(A∪ B) = 70

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

Substitute the known values:

70 = 45 + 38 − n(A ∩ B) ⇒ 70 = 83 − n(A ∩ B) ⇒ n(A ∩ B) = 83 − 70 = 13

So, n(A ∩ B) = 13

n(B − A) = n(B) − n(A ∩ B)

n(B − A) = 38 − 13 = 25

n (B − A) = 25