If n(A - B) = 24, n(B - A) = 32 and n(A ∩ B) = 10; find n(A ∪ B).

n(A - B) = 24

n(B - A) = 32

n(A ∩ B) = 10

∴ n(A - B) = n(A) - n(A ∩ B)

Putting the values, we get

24 = n(A) - 10

n(A) = 24 + 10

n(A) = 34

∴ n(B - A) = n(B) - n(A ∩ B)

Putting the values, we get

32 = n(B) - 10

n(B) = 32 + 10

n(B) = 42

∴ n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Putting the values, we get

n(A ∪ B) = 34 + 42 - 10

⇒ n(A ∪ B) = 76 - 10

⇒ n(A ∪ B) = 66

∴ n(A ∪ B) = 66