Axiom 1: Every team plays at leat two games  Axiom 2: Every game has at least two teams  Axiom 3 there exists at least one team  Questions: 1. What are the undefined terms in this axiom set? 2. Prove theorem 1: there exists at least one game 3. What is the minimum number of games?   4. Find to models that show that the statement " there are exactly two twam is independent of the axioms" 5. Find two models that show that the statement "every team plays every other team" is independent of the axioms.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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Axiom 1: Every team plays at leat two games 

Axiom 2: Every game has at least two teams 

Axiom 3 there exists at least one team 

Questions:

1. What are the undefined terms in this axiom set?

2. Prove theorem 1: there exists at least one game

3. What is the minimum number of games?  

4. Find to models that show that the statement " there are exactly two twam is independent of the axioms"

5. Find two models that show that the statement "every team plays every other team" is independent of the axioms. 

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