Let M be a model of Incidence Geometry. Prove that M has the Elliptical Parallel Property IFF M contains no parallel lines...
Just stumped on this one...help is greatly appreciated!!!
That is not the case. Different sets of axioms give different geometries.
In general, Incidence Axioms form a subset of the axiom set that establish the relation between points and lines.
Therefore, we need to know the set of axioms that underlie this question.
1) for every two distinct points, theres exists a unique line that is incident to both
2) For every live, there exists atleast two distinct points incident to that line
3. there exists 3 noncollinear points.
If all three of these axioms are satisfied within an interpretation, we have a model of Incidence Geometry.
Thus, the Elipptical Parallel Property States:
Given a line l and a point p not incident l, there is no line incident to p and parallel to l