- #1

- 221

- 0

R is a relation on X={a,b,c,d,f}

Starting from the bottom I have

vertex a which is related to vertex b and vertex c

Then I have vertex b related to vertex d and c related to vertex d

then I have vertex d related to vertex d and vertex f

So correct me if I am wrong but if I were to write out R as a set of ordered pairs I would have

R={(a,b), (a,c), (b,d), (c,d), (d,f), (d,e)}

If that is correct then how can this be a partial order when the definition of partial order says a relation is partial order iff R is reflexive? That relation is not reflexive since (a,a) is not an element of R (the same is true for b,c,d,e,f).

Next problem I have is how to tell if one element is comparable to another. If someone could give me a good intuitive idea of how to tell if two elements of R is comparable I would greatly appericate it.

Regards