We know that the walk and positive walk relations on a directed graph define relations, and the positive walk relation on a DAG defines a strict partial order. Answer each of the following and explain your answer.

a What sort of digraph has a walk relation that describes a total (linear) order?

b Given R is an equivalence relation, what would be the sim- plest way to draw a digraph that represents R with the walk relation? What would the digraph look like? What would each equivalence class look like?

c Why does a partial order have to be a DAG?