P2.8.4 Let A and B be sets and let RCAx B be a relation. The inverse relation of ove each of subset R-1 of B x A defined so that R-1 [(b,a) : (a, b) R]. Prove or dispr the following statements: (a) R is total if and only if R-1 is total. (b) R is well-defined if and only if R-1 is well-defined. (c) R is a function if and only if R-1 is a function. (d) If RCA x A, R is reflexive if and only if R-1 is reflexive. (e) If RC A x A, R is symmetric if and only if R-1 is symmetric. (f) If R A A, R is antisymmetric if and only if R-1 is antisymmetric. (g) If RCA x A, R is transitive if and only if R1 is transitive