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## Homework Statement

Determined if the following is an equivalence relation, if so describe the equivalence class.

The relationship [tex]C[/tex] on a group [tex]G[/tex], where [tex]aCb[/tex] iff [tex]ab=ba[/tex]

## Homework Equations

## The Attempt at a Solution

So i know there's 3 things to check: reflexive condition, symmetric condition, and the transitive condition.

The 1st two passed just by inspection, but I'm really stuck on the last one.

So if [tex]ab=ba[/tex] and [tex]bd=db[/tex] on a group [tex]G[/tex]does that imply [tex]ad=da[/tex]? That's how i set it up but I can't find how to (dis)prove it.