3. 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) | f(1) = g(1)} b) {(f, g) | f(0) = g(0) or f(1) = g(1)} c) {(f, g) | f(x) – g(x) = 1 for all x EZ} d) (f. g)| for some CEZ, for all x E Z, f(x) – %3D g(x) = C} e) {f, g) | f(0) = g(1) and f(1) = g(0)} %3D

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