# Partial Order relation conditions

A relation is Partial Order relation if it is

1. Reflexive

2. Anti-Symmetric

3. Transitive

I have never seen (example) Anti-Symmetric rule playing a decisive role in Partial Order relation as it is some what similar to Reflexive.

Can you provide an example clearing this doubt?

If a relation is symmetric, then you have $xRy$ if and only if $yRx$ ... that's not much of an 'order', is it? That is, you couldn't say that $x$ is ordered 'before' some other element $y$. Indeed, a relation that is reflexive, transitive, and symmetrical would be an equivalence relation, which is pretty much the opposite of what you'd want for an order.