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Consider the following relation on the set Z: xRy ? x2 + y is even. For...

Consider the following relation on the set Z: xRy ? x2 + y is even.


For each question below, if your answer is "yes", then prove it, if your answer is "no", then show a counterexample.


(i) Is R reflexive?


(ii) Is R symmetric?


(iii) Is R antisymmetric?

(iv) Is R transitive?


(v) Is R an equivalence relation? If it is, then describe the equivalence classes of R. How many equivalence classes are there?

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