1. Let R be a relation on Z defined by Ry if and only if x + y is even. Is R reflexive? Is R symmetric? Is R transitive? Prove or give a counterexample for each. Note: For transitivity, you may rely on the even/oddness of the sum of two odd numbers, the dif- ference of an even number and an odd number, the product of two even numbers, etc. without proving it. It is possible to use a direct line of proof- if you do you will get bonus points, but make sure not to spend too much time on it!

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