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[8] Consider the incidence axiom system. Determine which of the following interpretations of the undefined terms is a model of the system: i. Points
[8] Consider the incidence axiom system. Determine which of the following interpretations of the undefined terms is a model of the system: i. Points are dots on a sheet of paper, lines are circles drawn on the sheet of paper, incidence means that the dot lie on the circle. ii. Points are lines in the Euclidean 3-space, lines are planes in the space, incidence is the usual relation of a line lying on a plane. iii. Same as in ii., but the lines and the planes all pass through the origin. iv. Consider a given circle y in the Euclidean plane. Interpret points as all points inside 7, and lines as all open chords of y, and incidence as lie on.
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The first axiom of incidence is satisfied here Which states that for every pair of distinct points P ...Get Instant Access to Expert-Tailored Solutions
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