In the tournament described in Exercise 12 of Section 2.4, a top player is defined to be...

In the tournament described in Exercise 12 of Section 2.4, a top player is defined to be one who either beats every other player or beats someone who beats the other player. Use the WOP to show that in every such tournament with n players there is at least one top player.

Reference:

In a certain kind of tournament, every player plays every other player exactly once and either wins or loses. There are no ties. Define a top player to be a player who, for every other player x, either beats x or beats a player y who beats x.

(a) Show that there can be more than one top player.

(b) Use the PMI to show that every n-player tournament has a top player.

11. Let the “Fibonacci-2” numbers be defined as follows: