Let X = R\{(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 P(R) of equivalence classes of ~. This is called the real projective line. (C) Define a function which is a bijection from P (R) to the unit circle S = {(x, y) = R: x + y = 1}.