If n(A - B) = 30, n(B - A) = 48 and n(A ∩ B) = 15, find n(A ∪ B).

n(A - B) = 30

n(B - A) = 48

n(A ∩ B) = 15

∴ n(A - B) = n(A) - n(A ∩ B)

Putting the values, we get

30 = n(A) - 15

n(A) = 30 + 15

n(A) = 45

∴ n(B - A) = n(B) - n(A ∩ B)

Putting the values, we get

48 = n(B) - 15

n(B) = 48 + 15

n(B) = 63

∴ n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Putting the values, we get

n(A ∪ B) = 45 + 63 - 15

⇒ n(A ∪ B) = 108 - 15

⇒ n(A ∪ B) = 93

∴ n(A ∪ B) = 93