Using unions, intersections, and complements of sets, and the definitions of total and compound events in terms of sets, prove by applying the axiomatic definition of probability that for any three...

Using unions, intersections, and complements of sets, and the definitions of total and compound events in terms of sets, prove by applying

the axiomatic definition of probability that for any three arbitrary

events A , B, C:

(a) P(A U B U C) - P(A) + P(B) + P(C) - P(A OB) - P{B n

c) - P(c n A ) + P(AnBn c).

(b) P(A n B n C) = P(A)P(B\A)P(C\A n B).