Consider an n-player round robin tournament where every pair of players play each other exactly once. Assume that there are no ties and every game has a winner. Then, the tournament can be represented via a directed graph with n nodes where the edge x -> y means that x has beaten y in their game.

(a) Explain why the tournament graph does not have cycles (loops) of size 1 or 2.
(b) We can interpret this graph in terms of a relation where the domain of discourse is the set of n players. Explain whether the "beats" relation for any given tournament is always/sometimes/never:

(i) asymmetric
(ii) reflexive
(iii) irreflexive
(iv) transitive.