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Question: group i axioms of incidence 11 there is a unique...

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Group I. AXIOMS OF INCIDENCE 11. There is a unique line m incident to any two distinct points A, B. In other words, for any 2. Every line is incident to (that is, contains) at least two points. 13. There exists (at least) three non-collinear points (that is, three distinct points not all two distinct points A, B, there exists a unique line m containing A, B contained in the same line).Group B. AXIOMS OF BETWEENNESS B1. If B is between A and C, (written A*B*C), then A, B, C are three distinct points on a line, and also C B*A. (We may also write A-B-C or C-B-A. B2. For any two distinct points A, B, there exists a point C such that A*B*C 8 B3. Given three distinct points A, B, C are 3 distinct points lying on the same line, then one and only one of them is between the other two. B4. (Pasch) Let A, B, C be three non-collinear points, and let m be a line not incident to any of A, B, C. If m is incident to a point D lying between A and B, then it must also contairn either a point lying between A and Cor a point lying between B and C, but not both.e geometry in whic but Axiom B2 fails to be true. This shows that Axiom B2 is independent of the other axioms. Hint: Consider a proper subset of R2 as in Problem 2.]

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