URGENT!!! Relation that is asymmetric, symmetric and

aceminer · **Joined:** Sat, 20 Aug 2011 12:38:23 UTC **Posts:** 39

Hi guys, i am very new to relations.

Code:

Find a binary relation on Z251 which is not reflexive but is symmetric, antisymmetric and transitive.

My answer would be that it is a empty set.

Say R = {(1,1), (1,2), (2,2), (2,4)}
a R b <=> There exists c belong such that b = c x a
However, this relation would not be asymmetric.

Another answer i have would be that R = Empty set X Z251

Matt · **Joined:** Wed, 1 Oct 2003 04:45:43 UTC **Posts:** 9631

I agree that the empty relation satisfies all of those properties.

aceminer · **Joined:** Sat, 20 Aug 2011 12:38:23 UTC **Posts:** 39

Well, but what would be a proper answer for this?

outermeasure · **Posted:** Sat, 22 Oct 2011 05:41:49 UTC

aceminer wrote:

Well, but what would be a proper answer for this?

What is not proper about the empty relation?

In fact, you will necessarily have some element that is not related to anything else.

aceminer · **Joined:** Sat, 20 Aug 2011 12:38:23 UTC **Posts:** 39

Hmm... what i meant would be how should i present this in an answer which is proper. Or would an answer to be the question simply be it is an empty relation?

Shadow · **Posted:** Mon, 24 Oct 2011 22:04:08 UTC

aceminer wrote:

Hmm... what i meant would be how should i present this in an answer which is proper. Or would an answer to be the question simply be it is an empty relation?

All universal quantifier statements about empty sets are true.

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URGENT!!! Relation that is asymmetric, symmetric and

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