Math Problem Solver

Which of the following relations on the set of all functions from Z to Z are equivalence

relations. Verify each property of the equivalence relation.

(i) R1 = {(f, g) ∕ ∃c ∈ Z, ∀x ∈ Z, f(x) − g(x) = c}

(ii) R2 = {f, g}⁄f(0) = g(1), f(1) = g(0}