If n(A - B) = 30, n(B - A) = 20 and n(A ∩ B) = 10, find :

(i) n(A)

(ii) n(B)

(iii) n(A ∪ B)

Given:

n(A - B) = 30

n(B - A) = 20

n(A ∩ B) = 10

(i) n(A - B) = n(A) - n(A ∩ B)

Putting the values, we get

30 = n(A) - 10

n(A) = 30 + 10

n(A) = 40

(ii) n(B - A) = n(B) - n(A ∩ B)

Putting the values, we get

20 = n(B) - 10

n(B) = 20 + 10

n(B) = 30

(iii) n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Putting the values, we get

n(A ∪ B) = 40 + 30 - 10

⇒ n(A ∪ B) = 70 - 10

⇒ n(A ∪ B) = 60

Hence, n(A ∪ B) = 60