I think that there should be a canonical version of this question, and I suspect that one already exists. However, I cannot find such a thing.

What I am looking for is an answer which gives examples of relations which satisfy every possible combination of reflexive / transitive / symmetric (bonus points if there are also antisymmetric examples).

If no such question can be found, perhaps I will ask / answer it myself.

@MartinSleziak You are quite good at this kind of thing.

@XanderHenderson I remember that were some questions about one combination of these properties, but I do not remember one where all of them were collected.

For example, checking the frequent tab of relations+examples-counterexamples, I found this one: Example of a relation that is symmetric and transitive, but not reflexive.

This post collects three examples: Transitive, Reflexive, Symmetric Relations.

@MartinSleziak Thanks. I appreciate it. Neither of those (nor any of the other questions I've found from that list you posted) really seems to do the job. I guess I'll start work on a canonical dupe target.