Equivalence Relation on ℝ: xRy if x≥y | Symmetry and Transitivity Explained

[SMA_01]

Homework Statement

Determine whether the given relation is an equivalence relation on the set. Describe the partition arising from each equivalence relation:

xRy in ℝ if x≥y

Homework Equations

Reflexive: for all x in X, x~x
Symmetric: for all x,y in X, if x~y, then y~x
Transitive: for all x,y,z in X, if x~y, and y~z, then x~z

The Attempt at a Solution

I showed that it's reflexive, because x≥x

I'm kind of confused in regards to how to show that it's symmetric and transitive (if it is)?

Any help is appreciated, thanks.

 

[Dansuer]

The first thing i would do it's to try some value of x y and z to see if the property holds.