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.

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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Description: 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 game3. What is the

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

Problem 1CT

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

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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