Question: 1. Let X = {f: [0, 1] R} be the set of all real-valued functions on the closed interval [0, 1]. Define a relation

1. Let X = {f: [0, 1] R} be the set of

1. Let X = {f: [0, 1] R} be the set of all real-valued functions on the closed interval [0, 1]. Define a relation R on X by setting fRgf(1) = g(1). a Prove that R is an equivalence relation on X. (b) For a function f E X, let [f]R denote the equivalence class of f with respect to R. Find the cardinality of the set {[f]RfEX} of all equivalence classes modulo R. Justify your answer.

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