here's a problem from the current logic book I'm reading: Let (W,R) be a quazi-order and define ~ on W by putting s~t iff Rst and Rts. First (which i don't have a problem with) show ~ is an equivalence relation.
Part (b): Let [s] denote the equivalence class (mod ~ on W) containing s and define the following relation on the collection of equivalence classes: [s] =< [t] iff Rst. Show that this is well-defined.
Is the idea just to choose an arbitrary representative s' of [s] and t' of [t] and show that [s'] =< [t'] ? I guess I don't see how this isn't completely trivial since we automatically get [s'] = [s] and [t'] = [t] so using substitution [s'] =< [t']. Can someone show me what fallacious assumption i'm making in this argument? Maybe I'm confused because I've only seen problems asking to show an operation to be well-defined as opposed to some binary relation. Thanks for the help