Each of the following relations (denoted by ~) is an equivalence relation on N. Each has a finite number of equivalence classes; what are they, and how many of them are there?
(a) x ~ y means that x - y = 0 (mod 10)
(b) x ~ y means that x^2 - y^2 = 0 (mod 10)
(c) x ~ y means that x^3 - y^3 = 0 (mod 10)
Extra Credit: What will happen if the definition of ~ involves fourth powers, fifth powers, etc.?