Logic Axioms

Homework

Homework 5: Due Thursday October 18 Consider the following Axiom System

Axiom System IV

The Primitive Terms: player, team, and recruit

Axiom 1: There exists at least one team.

Axiom 2: Each team recruits exactly two players.

Axiom 3: For each team, there is exactly one other team such that no player is recruited by both.

Axiom 4: Each player is recruited by exactly two teams.

Prove the following theorems.

Theorem 1 There exist exactly four players.

Theorem 2 For each player, there exists at least one other player such that no team recruits both.

Theorem 3 For each pair of players, there exists at most one team recruiting both.

Theorem 4 For each player, there is exactly one other player such that no team recruits both.