Answer Happy

1 Round Robin A round-robin tournament is a tournament in which every player plays a single game (rock-paper-scissors, tennis, chess, etc.) with every other player. If S is a set of players, we encode a round-robin tournament as a binary relation R over S. Where aRb if and only if a beats b. If R represents a valid outcome of some round-robin tournament over S, we'll call R a round-robin relation over S. Question 1a ( 2 pts). Let S be a set with ∣S∣≥3. Let R be a round-robin relation over S. Which of the following properties does R have? (Select multiple) - Transitive - Symmetric - Asymmetric Connected Cyclic - Irreflexive Reflexive We can also view a round-robin tournament as a directed graph G=(S,R) where S, the set of players is the vertex set, and there is a directed edge from player u to player v if and only if u beats v. Question 1 b (4 4 pts). Let G=(S,R) be any round-robin tournament encoded as a directed graph. Show that if ∣S∣≥3, and G has some cycle, G has a cycle of length exactly 3 . Use the well-ordering principle.