Fix some n Z with n 2. Consider the relation R Z Z where xRy if n | (x y). a) (10 points) Show that R is reflexive. b) (10 points) Show that R is symmetric. c) (10 points) Show that R is transitive. d) (5 points) By parts, A, B and C, we know that R is an equivalence relation. This partition of the integers has a special name, Use set-builder notation with the format {f(k) : k Z}. That is, for each equivalence class, make a function of k that describes the elements of the set.

1. Fix some n Z with n 2. Consider the relation R Z Z where xRy if n | (x y).
a) (10 points) Show that R is reflexive.
b) (10 points) Show that R is symmetric.
c) (10 points) Show that R is transitive.
d) (5 points) By parts, A, B and C, we know that R is an equivalence relation. This partition of
the integers has a special name,
Use set-builder notation with the format {f(k) : k Z}. That is, for each equivalence class, make a
function of k that describes the elements of the set