Question

Proof question!
Axiom 1: There exists exactly 4 points
Axiom 2: Each point is in exactly 4 lines
Axiom 3: Each line contains exactly 2 points
Axiom 4: If a pair of points lie on a line then there exists exactly one other line to which they both belong.

Prove: For each point there exists exactly 4 lines not containing it.
How do I go about proving this?
The shape in question which fits this description is a square inscribed in a circle with the 4 points being at the 4 corners.

Answer 1

Have you attempted this problem yourself? It's rather large, and I don't see much work on it, so I can't really help.

Answer 2

I've been working on it with my group members and we came up with the shape that fits all 4 axioms and the statement to be proven, I just don't know how to translate that into logic

Answer 3

circle is a line, doesnt contain exactly 2 pionts, disproven by axiom 3

Answer 4

I asked the professor, he said it was correct. In Euclidean geometry you'd be right but the rules for Euclidean geomtery don't necessarily apply here