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How can I write down this property of relations 
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#1
Mar1014, 10:17 AM

P: 242

If I have a relation which is not only antisymmetric (##aRb\rightarrow{}\neg{}bRa##) but it also has a property that ##aRb\land{}bRc\rightarrow{}\neg{}cRa##. How can I be sure that this property holds for any string like that? So that ##aRb\land{}bRc\land{}cRd\rightarrow{}\neg{}dRa## without having to write it down forever?
I though writing down ##aRb\land{}bRc\rightarrow{}\neg{}cRa## was enough, but with just that I can't prove that ##cRd\rightarrow{}\neg{}dRa##. How can I define this property? Does it exist already? 


#2
Mar1014, 10:37 AM

Mentor
P: 18,061

Do you somehow want to derive the property [tex]aRb ~\wedge~bRc~\wedge~cRd~\rightarrow \neg dRa[/tex] from the previous two? I think you can easily find examples of relations that are asymmetric and satisfy the second property and such that the above property doesn't hold. 


#3
Mar1014, 02:40 PM

P: 242

Sorry, I'm having a hard time explaining this.. I want to create a relation for which asymmetry holds as well as this other property that if a relates to b relates to c relates to d and so on, then not only do they not relate the other way due to asymmetry but also that the last element in the "string" does not relate to any of the previous ones (eg d does not relate to b and a, and c does not relate a) which I don't think you can derive from asymmetry. My question is: how can I write this property down simply? 


#4
Mar1114, 01:43 PM

HW Helper
Thanks
PF Gold
P: 7,583

How can I write down this property of relations
http://en.wikipedia.org/wiki/Partially_ordered_set http://staff.scm.uws.edu.au/cgibin/...gi?page=20&key 


#5
Mar1114, 09:02 PM

P: 242

The relation I am looking for satisfies the following conditions:



#6
Mar1214, 05:12 AM

P: 907




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