Suppose that if PE 1 then E which by the way is not always

Suppose that if P(E) = 1 then E = (which by the way, is not always true). Let A be a subset of B, with P(A) = P(B). Prove that necessarily A = B.

Just wondering if I can solve this by proving that B is a subset of A.

Solution

Yes you can solve like that way because if there are equal it doesnt matter if A is a subset of B or B is a subset of A

they will be the same