Let S be the sample space, and consider the following three axioms of probability: P(A) 0 for all events A S, P(S) = 1. If A and B are disjoint events, then P(A B) = P(A) + P(B).

Using these axioms, prove that:

1. P(A) = 1 P(A), where A is complement of A.

2. If A B, then P(A) P(B)