The answer for this turns out to be only irreflexive. However, how is this not transitive? The definition I have for transitive states "whenever there is a path from x to y then there must be a direct arrow from x to y". So for the above graph, if there exists a path from one point to another, then there should be a direct arrow. Well that appears to be the case for the above image, no? Theres a path from C to B, and there is a direct arrow. There is no path from C to E, so no arrow needed. No path from B to C, B to D, so no arrows needed here. There is a path from Z to A and there is also a direct arrow, and same for A to Z. Am I misunderstanding this?
For a transitive relation the following are equivalent:
- Being a strict partial order
Does this mean that if a relation is transitive, then it is also irreflexive? If thats the case, then shouldn't the above graph then be transitive?