A tournament occurred where every player played every other player once. A player is called strong if any other player was either beaten by the strong player or did beat the strong player but was beaten by another player who was beaten by that strong player.

(a) Formalize this using logic symbols, with the set of players, and B(x.y): x beaty. 

(b) Take the denial symbolically and then as a written statement.

 (c) Provide an explanation why there will always be at least one strong player.