Given the following Axioms of Fano's geometry:
1. There exists at least one line
2. Each line...
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Given the following Axioms of Fano's geometry:
1. There exists at least one line
2. Each line is on exactly 3 points
3. Not all points are on the same line
4. Each pair of points are on exactly one line
5. Each pair of lines are on at least one point
a) Prove every point is on exactly three lines
b) What geometries are possible if you eliminate Axiom 5?
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ANS a Pick a line l exists by Axiom 1 Choose any point P not on l exists by Axiom 3 Since l has 3 points Axiom 2 joining P to each of them gives three distinct lines through P by
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