Prove that the incident axioms are independent, that is:
Indicate geometry model such that:
- b) the l2 axiom does not hold and the l1 and l3 axioms do
I1. For any two distinct points A, B there exist a unique line l containing A, B.
I2. Every line contains at least two points.
l3. There exist three noncollinear points (that is, three points not all contained in a single line).
Anyone have any idea?
what about case b)?
This geomtery will do. Points $A$, $B$, $C$ fulfill L3, The lines $\ell_1,\ell_2,\ell_3$ satisfy L1. The line $\ell_0$ defy L2.