/15 points) de ne a binary operation on z, as follows x y = xy (for all x, y z). Why or why not? (c) show that 1 is an identity for . /14 points) consider z with some relation r. also, let a, b z. (a) let arb if and only if a b. r is not an equivalence relation. Why? (b) let arb if and only if a b is divisible by 2. /15 points) let f : a a and g : a a for some (non-empty) set a. (a) de ne f is onto . (b) suppose that f and g are both one-to-one. Show that f g is one-to-one. (c) let h : z z where h(x) = 2x + 1. /14 points) prove one of the following (choose i. or ii: let u be a set, a u , and b u .
