Prove that for arbitrary events A, B, C, the following statements do not hold in general:_ (a) P(A\C) + P(A\C) = 1. (b) P(A\C) + P{A\C) = 1. (c) P(A U B\C) = P(A\C) + P(B\C). (d) P(A H B\C) =...

Prove that for arbitrary events A, B, C, the following statements do

not hold in general:_

(a) P(A\C) + P(A\C) = 1.

(b) P(A\C) + P{A\C) = 1.

(c) P(A U B\C) = P(A\C) + P(B\C). (d) P(A H B\C) = P(A\C)P(B\C). Investigate conditions, if any, under which each statement is correct.