# Equivalence Relations and Classes

For m, n, in N define m~n if m^2 ? n^2 is a multiple of 3.

(a.) Show that ~ is an equivalence relation on N.

(b.) List four elements in the equivalence class [0].

c) List four elements in the equivalence class [1].

(d.) Are there any more equivalence classes. Explain your answer.

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