Intransitive...Irreflexive...

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Reply Sat 5 Dec, 2009 07:39 pm
Hi there.

I need to show by tableau method that an intransitive relation is also irreflexive.

Here is what I know:

-an intransitive relation basically explains the scenario wherein object1 is connected to objected2, and object 2 is connected to object3, but that object 1 is not connected to object3


For example, x is the father of y, and y is the father of z, but x is not the father of z

-in the case of irreflexivity, I think this means that if x and y stand for men, "Rxy," will mean that "x is the father of y." The way I understand "irreflivity" is that when not element is set in relation to itself...so in the case of the example I provided above, I know that all intransitive relations are irreflexive, but I am not sure how to go about showing this by tableau.

I think I would be working with something to the effect of...


x∀y∀z is not Rxz
x∀y∀z[Rxy ^ Ryz]
 
Horace phil
 
Reply Sun 6 Dec, 2009 04:55 pm
@Horace phil,
I start with this, right?



---------- Post added 12-06-2009 at 08:37 PM ----------

I've been doing some more thinking.

For the relation to be non-transitive all we need is 1 case where Rxy ^ Ryz > notRxz

so this would be read as:

ExEyEz (Rxy ^ Ryz > not Rxz)

For the relation to be non-reflexive , it must be that there is at least one case where Rww (or could I write this as Rxx) is not true

Ew(notRww)

So we get:

ExEyEz (Rxy ^ Ryz > Rxz) > Ew(notRww)

Before when I said AxnotRxx what I was saying was that every x fails to be reflexive, but i think all we need to do is show simply once cause where it fails...

I'm just trying to figure this stuff out. http://forums.philosophyforums.com/templates/images_default/smilies/smile.gif
 
cerafagg
 
Reply Tue 22 Mar, 2011 05:42 pm
@Horace phil,
Hey Horace.. I know you havent used this forum for a while, but if you still get this message, can you message me? I need some help with philosophy. My email is [email protected]. Thx i would really appreciate it!
 
 

 
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