Prove the following statements. Show your working.

(i) If P(A|B, C) = P(B|A, C), then P(A|C) = P(B|C)

(ii) If P(A|B, C) = P(A), then P(B, C|A) = P(B, C)

(iii) If P(A, B|C) = P(A|C) P(B|C), then P(A|B, C) = P(A|C)