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Given the following Axioms of Fano's geometry: 1. There exists at least one line 2. Each line...

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Basic Math

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?

Answer & Explanation Solved by verified expert
4.4 Ratings (736 Votes)
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    See Answer
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