Difficult algabraeic probability manipulation question

Question

Suppose that A and B are independent events. Show algebraically, using only the

probability axioms and properties, and basic set-theoretic results given in the lectures,

that  A and B

are independent events.

Answer 1

A and B are independent events if P(A/B) + P(A)

and P(B/A) = P(B)

The probability of B doesn't change if A occurs.

The probability of A doesn't change if B occurs