Question

If n(P(A)) = 1024, n(A ∪ B) = 15 and n(P(B)) = 32, then find n(A ∩ B)

Answer 1

Given n(P(A)) = 1024, n(A ∪ B) = 15, n(P(B)) = 32

n(P(A)) = 1024 = 2¹⁰ n(A) = 10

n(P(B)) = 32 = 2⁵ = n(B) = 5

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

15 = 10 + 5 – n(A ∩ B)

15 = 15 – n(A ∩ B)

n(A ∩ B) = 0