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?


1 Answer 1


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.

So, by making the relation anti-symmetric (or asymmetric, to get a strict order), you rule out such possible symmetry, and you can actually start talking about an order.

  • $\begingroup$ one last thing if instead of anti-symmetric if i use asymmetric does it allow Reflexive elements in my relation. $\endgroup$
    – codenut
    Commented Oct 14, 2017 at 21:33
  • 1
    $\begingroup$ @codenut No, it does not. Asymmetry implies irreflexivity. And so it is actually reflexivity that isn't really 'characteristic' of an order. It is the combination of anti-symmetry/asymmetry plus transitivity that is characteristic of orders. $\endgroup$
    – Bram28
    Commented Oct 14, 2017 at 21:48

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