Creating theorems from the given axioms

[dezzi1]

Given the following axioms, create 3 theorems.

Axiom 1: Each game is played by two distinct teams.
Axiom 2: There are at least four teams.
Axiom 3: At least six games are played.
Axiom 4: Each team plays at most four games.

I have already proven each axioms independence.

These are the following theorems I have:
1. There are at least 2 teams that play a game
2. If there are exactly 4 teams then there at most 8 games

I have completely proven theorem 1. I just need help proving theorem 2 and creating/proving a third theorem.

Any help will be greatly appreciated!

 

[Greg]

Hello and welcome to MHB, dezzi! :D

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Can you post what you have done so far?