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Define a relation R on Z by (x, y) ∈ R if, and only if, x − y is odd. Is R an equivalence relation? Z meaning the set of all integers I really dont have a good grasp on reflexive, symmetric, or transitive relations.

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  • $\begingroup$ Welcome to MSE. Please let us know what you've tried and where you are stuck so that we can point you in the correct direction. The point of this forum is to help you along the way, not do all the work. $\endgroup$ – Tom Oct 7 '16 at 1:27
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Hint:

Is it true that $(x,x) \in R$?

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This relation lacks reflexiveness; $(x,x)\not\in R$. So it is not an equivalence relation.

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