Problem #PRU-30826

Problem

Several teams played a volleyball tournament amongst themselves. We will say that team $A$ is better than team $B$, if either $A$ has either beaten team $B$, or there exists such a team $C$ that was beaten by $A$, whilst $C$ beat team $B$.

a) Prove that there is a team that is better than all.

b) Prove that the team that won the tournament is the best.