For each statement below indicate if it is true or false and explain why. Most of the credit in this problem is for the explanations. Please read the statements carefully.

a. If B C and R is a relation on A x B then R is a relation on A x C. b. If B C and f is a function from A to C then f is a function from A to B.

c. If R is a relation on A x B then we may define R' = {(b, a) | (a, b) R} and R' will be a relation on B x A.

d. If f is a function A -> B then we may define g = {(b, a) | (a, b) f} and g will be a function g: B -> A.