Seeing if a relation on set Z is a equivalence relation

Question

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.

Answer 1

Hint:

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

Answer 2

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