Instructions: Show that there are essentially only 2 models for the following axiom system:
Undefined terms: point, adjacent to, and color.
1. There are exactly 5 points.
2. If point A is adjacent to point B, then point B is adjacent to point A.
3. If point A is not adjacent to point B, then there exists a point C to which A and B are mutually adjacent.
4. Each point is assigned a color, red or green.
5. Any two adjacent points are assigned to different colors.
R = red point, G = green point
The models I came up with were:
Model 1: G R G R G
Model 2: R G R G R
Another model could be a vertical orientation, but it would essentially be the same just flipping the models up. The order of the points would still be the same. There is no other way I could think to represent this axiom system where all 5 axioms were satisfied. Is my answer even remotely close to being possibly correct?
Thank you for your time.