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Exercise 4.2 Vector Spaces Which of the following sets are vectors spaces? a) The set of points S = {(r, y) : y = I, IER). b) The set of points S = {(x, y) : y = 1/x}. c) The set of polynomials of infinite degree. d) The set of infinite sequences { I1, 12, 13, . . . } where each r; E R. e) The set of constant functions S = {f(x) : f(x) = c some fixed ce R} In each case assume that the scalar field for multiplication is the real numbers. Show your reasoning