I get that something such as R={(0, 0),(0, 1),(1, 1),(1, 2),(0, 2),(2, 2)} on the set {0, 1, 2} would be reflexive, anti-symmetric, transitive and a total ordering, however things that are less cut and dry such as:
Suppose that F is a set of files, and R is the relation on F where fRg if g depends on f. That is, f must come before g. Noting that the dependency may not be direct - g might depend on f through some intermediary files such as h or j.
I can tell that it is transitive (based on last part of question), that is fRh ∧ hRg → fRg, but am unsure how to prove whether or not R is reflexive, irreflexive, symmetric, anti-symmetric, partial ordering or total ordering (strict or not) and the equivalence class.
How would I go about identifying these?