Question

If n(A) = 300, n(A ∪ B) = 500, n(A ∩ B) = 50 and n(B’) = 350, find n(B) and n(U)

Answer 1

Given,

n(A) = 300, n(A ∪ B) = 500, n(A ∩ B) = 50 and n(B’) = 350

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

500 = 300 + n(B) – 50

500 = 250 + n(B)

500 – 250 = n(B)

250 = n(B)

∴ n(B) = 250

n(U) = n(B) + n(B)’

250 + 350 = 600

∴ n(B) = 250 and n(U) = 600