Homework: Incidence Axioms.

1. For the `Fe-Fo' axiom system, create a model such that
   
   
   1. all the Fe-Fo system axioms hold except Axiom 3.
      
      
   2. all the Fe-Fo system axioms hold except Axiom 4.
   
   (Note: you can maintain or alter the definitions of the Fe's and the Fo's, and the relations as given in the examples.)
   
   Problems 2 - 4 use the incidence axiom system for points, lines and planes. Write each proof in both paragraph and two-column format.
   
   
2. Prove: If two lines intersect, then they intersect in at most one point.
   
   
3. Given a line and a point not on the line, there is exactly one plane containing the line and the point. (Hint: must show that a plane exists that contains the point and the line and then that there is only one plane. )
   
   
4. Prove: A geometry that satisfies the Incidence Axioms must contain at least six lines and at least four planes.
   
   Problem 5 uses the incidence axioms for the plane.
   
   
5. Justify the assertion that the statement ``every line contains the same number of points'' is independent from the incidence axioms.

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