6.6 In an incidence geometry, consider the relationship of parallelism, "l is parallel to m," on the set of lines. (a) Give an example to show that this need not be an equivalence relation. (b) If we assume the parallel axiom (P), then parallelism is an equivalence relation. (c) Conversely, if parallelism is an equivalence relation in a given incidence geom- etry, then (P) must hold in that geometry.

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