Fix some n Z with n 2. Consider the relation R Z � Z where xRy if.pdf

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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.

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