If n(A) = 100 and n(A∩B) = 40, what is n(A∩B′)?

Question

This is the entire question.. no information on universe or n(B)

Answer 1

Because AB and AB' are mutually exclusive and their union is A,

n(AB) + n(AB') = n(A)

Thus, n(AB') = n(A) - n(AB) = 100 - 40 = 60

(The below seems totally unnecessary, but if you would like a proof that AB and AB' are mutually exclusive and their union is A, and the sum formula is correct,

let the universe be U.

Then, to show mutually exclusive, ABAB' = AABB' = A∅ = ∅

AB ∪ AB' = A(B ∪ B') = AU = A

As AB ∪ AB' = A,

n(AB) + n(AB') - n(ABAB') = n(A)

Yet, n(ABAB') = 0;

therefore, n(AB) + n(AB) = n(A) )