- Assume the four axioms of incidence geometry. Prove the following claims:
(a) Given a line L and a point A that lies on L, there exists a point B that lies on L
and is distinct from A.
(b) Given any line, there exists a point that does not lie on it. - Define the Three-Ring Geometry as follows: a point is any one of the numbers 1, 2,
3, 4, 5, 6; a line is any one of the sets {1, 2, 5, 6}, {2, 3, 4, 6}, or {1, 3, 4, 5}; and lies
on means is an element of. Provide a sketch of the geometry and determine if it is a
model of incidence geometry. Explain why?
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