p.609, icon at Example 2 # 2. Let A be the set of all points in the plane with the origin removed. That is, Define a relation on A by the rule: A = {(x, y)|x, y = R} - {(0,0)}. (a, b)R(c, d) ↔ (a, b) and (c, d) lie on the same line through the origin. (a) Prove that R is an equivalence relation. (b) Describe the equivalence classes arising from the equivalence relation R in part (a). (c) If A is replaced by the entire plane, is R an equivalence relation?

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A:

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