Suppose that f : R → R is a function on R. Define a relation Rf on R by the rule (x, y) E Rf if andonly 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;:

Answered: a. Prove that Rf is an equivalence…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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,: