Let n ∈ Z⁺ and let ~ be defined on Z by r ~ s if and only if r - s is divisible by n, that is, if and only if  r - s = nq for some q ∈ Z.
a. Show that ~ is an equivalence relation on Z. (It is called "congruence modulo n" just as it was for Z⁺.
b. Show that, when restricted to the subset Z⁺ of Z, this ~ is the equivalence relation, congruence modulo n, of Example 0.20.
c. The cells of this partition of Z are residue classes modulo n in Z. Repeat Exercise 35 for the residue classes modulo in Z rather than in Z⁺ using the notation { • • • . #. #, #. • • •} for these infinite sets.