Which of these relations on the set of all functions from

Chapter 8, Problem 8.5.3

(choose chapter or problem)

Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(f, g) I 1(1) = g(1)} b) {(f, g) I 1(0) = g(O) or 1(1) = g(1)} c) {(f, g) I I(x) - g(x) = I for all x E Z} d) {(f, g) I for some C E Z, for all x E z, I(x) g(x) = C} e) {(f, g) I 1(0) = gel) and 1(1) = g(O)}