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A projective plane is a plane (S,L ) satisfying the following four axioms. P1. For any...

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Advance Math

A projective plane is a plane (S,L ) satisfying the followingfour axioms. P1. For any two distinct points P and Q there is oneand only one line containing P and Q. P2. For any two distinctlines l and m there exists one and only one point P belonging tol∩m. P3. There exist three noncollinear points. P4. Every linecontains at least three points.

Let π be a projective plane. Using P1 − P4, show that π containstwo distinct lines l and m and a point P such that P does not lieon l or m.

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