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1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a)...

1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a) Explain why R is not an equivalence relation. b) Explain why S is not an equivalence relation. c) Find S ◦ R. d) Show that S ◦ R is an equivalence relation. e) What are the equivalence classes of S ◦ R?

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