# Seeing if a relation on set Z is a equivalence relation

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