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