a. It is always true, for any events A, B, that P(A B) < P(A) +

Question:

a. It is always true, for any events A, B, that P(A  B) < P(A) + P{B). Why? Explain briefly with words or a very clear picture.
b. Is it always true that P(A  B  C) < P{A) + P(B) + P(C)?. If so, explain why, either using words or a very clear picture. If not, please give a counterexample.