For each of the following expression, derive an equivalent expression in terms of only the given conditional distributions, using the given conditional independence assumptions. If it is not possible, say so. 

a. Express P(A, B | C) in terms of P(A), P(A | C), P(B | C), P(C | A, B) given no conditional independence assumptions. 

b. Express P(B | A, C) in terms of P(A), P(A | C), P(B | A), P(C | A, B) and no conditional independence assumptions. 

c. Express P(C) in terms of P(A | B), P(B), P(B | A, C), P(C | A) given that A and B are absolutely independent. 

d. Express P(A, B, C) in terms of P(A | B, C), P(B), P(B | A, C), P(C | B, A) given that A is conditionally independent of B given C.