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incidence axiom 1: for each two distinct points there exists a unique line on both of them
incidence axiom 2: for every line there exists at least two distinct points on it
incidence axiom 3: there exist at least three distinct points
incidence axiom 4: not all points lie on the same line

Prove if P is any point then there are at least two distinct lines l and m such that P lies on both l and m

assume the euclidean parallel postulate holds. then prove that if l m and n are distinct lines such that n and m intersect and l is parallel to m then l also intersects n

consider a finite model for incidence geometry plus the additional axiom: every line has exactly three points lying on it.---what is the minimum number of points that exist in such a geometry?

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