Let X = R{(0,0)} and consider the relation on X defined by ~ (x1, y1)~ (x2,...

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Let X = R²\{(0,0)} and consider the relation on X defined by ~ (x1, y1)~ (x2, Y2) AER s.t. (x1, y1) = (x2, Ay2). . (A) Prove that is an equivalence relation. . (B) Give an explicit description of the set P¹(R) of equivalence classes of ~. This is called the real projective line. ● (C) Define a function which is a bijection from P¹ (R) to the unit circle S¹ = {(x, y) = R²: x² + y² = 1}. Let X = R²\{(0,0)} and consider the relation on X defined by ~ (x1, y1)~ (x2, Y2) AER s.t. (x1, y1) = (x2, Ay2). . (A) Prove that is an equivalence relation. . (B) Give an explicit description of the set P¹(R) of equivalence classes of ~. This is called the real projective line. ● (C) Define a function which is a bijection from P¹ (R) to the unit circle S¹ = {(x, y) = R²: x² + y² = 1}.

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Lets address each part of the question one by one A Prove that is an equivalence relation To prove that a relation is an equivalence relation we must show that it satisfies three properties reflexivit... View the full answer