Which of these rela tions on the set of all functions from

Chapter 13, Problem 3E

(choose chapter or problem)

Problem 3E

Which of these rela tions 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(l) = g(l )}

c){( f, g) | f(x) - g(x) = 1 for all x ∈ Z}

d){( f, g) | for some C ∈ Z, for all x ∈ Z, f(x) - g(x) = C}

e){( f, g) |f(0) = g(1) and f(1) = g(0)}