Question

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A’ ∩ B’) = 5, find

(i) n(A ∪ B)

(ii) n(A ∩ B)

(iii) n(A’ ∩ B)

(iv) n(A ∩ B’)

Answer 1

n(X) = 50, n(A) = 35, n(B) = 20, n(A’ ∩ B’) = 5

(i) n(A ∪ B) = n(X) – [n(A ∪ B)’] = n(X) – n(A’ ∩ B’)

= 50 – 5

= 45

(ii) n(A ∩ B) = n(A) + n(B) – n(A ∪ B)

= 35 + 20 – 45

= 10

(iii) n(A’ ∩ B) = n(B) – n(A ∩ B)

= 20 – 10

= 10

(iv) n(A ∩ B’) = n(A) – n(A ∩ B)

= 35 – 10

= 25