(i) If n(A) = 25, n(B) = 40, n(A ∪ B) = 50 and n(B’) = 25, find n(

1.	(i) If n(A) = 25, n(B) = 40, n(A ∪ B) = 50 and n(B’) = 25, find n(A ∩ B) and n(U).(ii) If n(A) = 300, n(A ∪ B) = 500, n(A ∩ B) = 50 and n(B’) = 350, find n(B) and n(U).
Answer» (i) n(A ∩ B) = n(A) + n(B) – n(A ∪ B) n(A ∩ B) = 25 + 40 – 50 = 65 – 50 = 15 n(U) = n(B) + n(B’) = 40 + 25 = 65 (ii) n(U) = n(B) + n(B’) n(A ∩ B) = n(A) + n(B) – n(A B) n(B) = n(A ∪ B) + n(A ∩ B) – n(A) = 500 + 50 – 300 = 250 n(U) = 250 + 350 = 600

(i) If n(A) = 25, n(B) = 40, n(A ∪ B) = 50 and n(B’) = 25, find n(A ∩ B) and n(U).(ii) If n(A) = 300, n(A ∪ B) = 500, n(A ∩ B) = 50 and n(B’) = 350, find n(B) and n(U).

Answer»

(i) n(A ∩ B) = n(A) + n(B) – n(A ∪ B)

n(A ∩ B) = 25 + 40 – 50 = 65 – 50 = 15

n(U) = n(B) + n(B’) = 40 + 25 = 65

(ii) n(U) = n(B) + n(B’)

n(A ∩ B) = n(A) + n(B) – n(A B)

n(B) = n(A ∪ B) + n(A ∩ B) – n(A) = 500 + 50 – 300 = 250

n(U) = 250 + 350 = 600