1. Consider the following axiomatic system: A1: Each point is incident to exactly 2 lines. A2:...

1. Consider the following axiomatic system:

A1: Each point is incident to exactly 2 lines.

A2: For each pair of distinct lines, there is a point that is incident to both lines.

A3: There are exactly 5 lines.

(a) Pick one of the three axioms and prove that it is independent from the other axioms in the system. Be sure to justify your answer.

(b) Find the minimum number of points present in a model for this system. Be sure to justify your answer using the axioms given above.

Expert Solution

Colby Messinger answered 5 months ago

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