We can define a three-point geometry by letting the set of points {A, B, C} represent the plane. Then the lines will be pairs of points. We will accept the following three postulates.
Postulate 1: There are exactly three points.
Postulate 2: Every pair of points is on a line.
Postulate 3: Every line contains exactly two points.
Answer the following questions about this three-point geometry. Justify your answers.
a. How many lines are in this geometry?
b. If two lines intersect, how many points do they have in common?
c. Are there parallel lines in this geometry?
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