Empty Relation

[rizing_starz4]

Just for clarification before the test, the empty relation has all of
the properties (reflexive, irreflexive,symmetric, etc.), right?

[Ian W.]

It depends on what A is! If R is a relation on A, R = nil and A is non-
empty then, for example, the empty relation is not reflexive:

A = {a}
R = nil

forall x in A : R(x,x) is false, because a in A but R(a,a) does not
hold.

So it is not necessarily the case that the empty relation satisfies
all these properties. Remember: a relation R is always defined with
respect to some set A.

Ian

[rizing_starz4]

Oh right. I think I got confused. The empty relation is always
irreflexive, symmetric, asymmetric, antisymmetric, and transitive no
matter what A is, though, right?

> > the properties (reflexive, irreflexive,symmetric, etc.), right?- Hide quoted text -
>
> - Show quoted text -

[Ian Wehrman]

On Fri, May 15, 2009 at 9:56 AM, rizing_starz4 <rizing...@yahoo.com> wrote:
>
> Oh right. I think I got confused. The empty relation is always
> irreflexive, symmetric, asymmetric, antisymmetric, and transitive no
> matter what A is, though, right?

Yes.