a. Prove that Rf is an equivalence relation. b. Suppose that f is the squaring function defined by f(x) = x². For a fixed real number r determine the equivalence class [r]R,:

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Suppose that f : R → R is a function on R. Define a relation Rf on R by the rule (x, y) E Rf if and
only if f(x) = f (y). Explicitly, we have R = {(x,y) E R² | ƒ(x) = f(y)}.
a. Prove that Rf is an equivalence relation.
b. Suppose that f is the squaring function defined by f(x) = x². For a fixed real number r e R,
determine the equivalence class [r]R;:
Transcribed Image Text:Suppose that f : R → R is a function on R. Define a relation Rf on R by the rule (x, y) E Rf if and only if f(x) = f (y). Explicitly, we have R = {(x,y) E R² | ƒ(x) = f(y)}. a. Prove that Rf is an equivalence relation. b. Suppose that f is the squaring function defined by f(x) = x². For a fixed real number r e R, determine the equivalence class [r]R;:
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