Consider the following axiom system in which student, committee and “on” are the undefined terms. A1. There exists exactly four students. A2. Any two distinct student have exactly one committee on both of them. A3. Each committee is on exactly two students. 1. Draw the model of the finite geometry 2. How many committees are there in the system? Show how did you get your answer 3. Write a simple proof of your answer.
Consider the following axiom system in which student, committee and “on” are the undefined terms. A1. There exists exactly four students. A2. Any two distinct student have exactly one committee on both of them. A3. Each committee is on exactly two students. 1. Draw the model of the finite geometry 2. How many committees are there in the system? Show how did you get your answer 3. Write a simple proof of your answer.
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.1: Sets And Geometry
Problem 35E
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Consider the following axiom system in which student, committee and “on” are the undefined terms. A1. There exists exactly four students. A2. Any two distinct student have exactly one committee on both of them. A3. Each committee is on exactly two students.
1. Draw the model of the finite geometry
2. How many committees are there in the system? Show how did you get your answer
3. Write a simple proof of your answer.
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