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Prove that the axiomatic set for Fano's 7 point/line geometry is independent

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Basic Math

Prove that the axiomatic set for Fano's 7 point/line geometry isindependent

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Axioms for Fanos Geometry Undefined Terms point line and incident Axiom 1 There exists at least one line Axiom 2 Every line has exactly three points incident to it Axiom 3 Not all points are incident to the same line Axiom 4 There is exactly one line incident with any two distinct points Axiom 5 There is at least one point incident with any two distinct lines Fanos Theorem 1 Two distinct lines    See Answer
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