Question: Problem 5. (20 points) Define A = R x R - {(0, 0) } the set of all points in the two-dimensional Cartesian coordinate plane

Problem 5. (20 points) Define A = R x R - {(0, 0) } the set of all points in the two-dimensional Cartesian coordinate plane minus the origin. Define a relation ~ between two points (x1, y1) and (x2, y2) by saying they are related if they lie on the same line passing through the origin. That is, (21, y1) ~(x2, y2) iff there exists some > # 0 (x1 = Xx2 A y1 = Xy2). a) (12 points) Prove that relation ~ is an equivalence relation on the set A. b) (8 points) Give a description of what each part in the resulting partition looks like

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