Question: Just as the difference rule gives rise to a formula for the probability of the complement of an event, so the addition and inclusion/exclusion rules give rise to formulas for the probability of the union of mutually disjoint events and for a general union of (not necessarily mutually exclusive) events.
a. Prove that for mutually disjoint events A and B,
P(A ∪ B) = P(A) + P(B).
b. Prove that for any events A and B.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B).