Does symmetry and transitivity imply reflexivity? — The Ross Programs

A common misconception is that symmetry and transitivity together imply reflexivity, making reflexivity redundant. The "empty relation" dramatically demonstrates this is not the case.

[abaskm]

I was scouring all over the web looking to understand this logic, but felt something was missing from those answers. Your video brought it home. Thanks!

[joelneely]

Let X={a, b, c} and ~ be {(b, b), (b, c), (c, b), (c, c)}. This example is symmetric and transitive but not reflexive. I like having a non-vacuous example as well.