Can you prove this? Using Boolean algebra and rules of probability

Question

P(A + B) = P(A) + P(B) − P(A B).

Answer 1

P(A U B) =

1 - P(A'B') =

P(AB) + P(AB') + P(A'B) + P(A'B') - P(A'B') =

P(AB) + P(AB') + P(A'B) =

P(AB) + P(AB') + P(A'B) + P(AB) - P(AB) =

(P(AB) + P(AB')) + (P(AB) + P(A'B)) - P(AB) =

P(A) + P(B) - P(AB)