b and c please!

1 Let X be a set. A binary relation ~ is called an equivalence relation if: i) r~T; ll) x ~ y implies y~ i1) x ~ y and y~ Z limpliesT~. A function f with domain X is called a representing function for ~ if x ~ y exactly when f(x) = f(y) a) Let n 1 be an integer. Find a representing function when x ~ y iff x-y is a multiple of n. b) Show that every equivalence relation has a representing function. c) Suppose X has n elements. Consider two methods for storing an equivalence relation on a computer: a) a 0-1 array indicating, for each pair, whether the relation holds between them or not; b) a succinct tabulation of the representing function. Which uses less space