12. Interpret a \"tree\" as a committee and a row\" as a person. Use the theory

Question

12. Interpret a "tree" as a committee and a row" as a person. Use the theory developed for the axiom system A-E to assign 6 people Arias, Braun, Chang, Desai, Enoki, and Flynn to 4 committees. 13. Define a triangle to be a set of three lines, each pair of which shares exactly one point, called a vertex. How many triangles are there in the six-point model? 14. Two lines are parallel if they have no points in common. Consider the following parallel postulate: given a line c and a point P not on C, there is a unique line M that contains P and is parallel to C. Do the 4-point geometry and 6-point geometries satisfy this postulate?

Explanation / Answer

Now as per given assumption let us first right the axioms

Atleast one commitee

Person belongs to exactly two committee

Comittee belongs to atleast one person

Any 2 committe have exactly 1 person in common

For every person there is exactly one other person for which there is no committe in common.

And as per above Axioms we can assign as belwo

1 Arias , Enoki , Chang
2 Braun , Flynn, Enoki
3 Chang , Arias, Desai
4 Desai , Braun , Flynn

Here lets say committe are from 1 to 4 so as per axioms above would be the setting.

Arais - Belongs to two committe and uncommon perosn is Braun
Braun - Belongs to two committe and uncommon perosn is Arias
Chang - Belongs to two committe and uncommon perosn is Braun

Desai - Belongs to two committe and uncommon perosn is Enoki

Enoki - Belongs to two committe and uncommon perosn is Desai

Flynn - Belongs to two committe and uncommon perosn is Chang

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