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,:
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,:
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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Question
![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;:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039207b8-632a-4dc4-a3c4-fd77b3c684b4%2F48b3223d-9e72-41e4-9067-3cbb1fe10848%2Fhhcb7ph_processed.png&w=3840&q=75)
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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