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Problem 2 Let T be the relation on R x R defined by (x, y) T (a, b) if x² - y = a²-b. Part (a): Prove that T is an equivalence relation on RX R. Part (b): Sketch the equivalence class of (2,1) (this will be a curve in the plane).

Problem 2 Let T be the relation on R x R defined by (x, y) T (a, b) if x² - y = a²-b. Part (a): Prove that T is an equivalence relation on RX R. Part (b): Sketch the equivalence class of (2,1) (this will be a curve in the plane).

Advanced Engineering Mathematics
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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Problem 2 Let T be the relation on R x R defined by (x, y) T (a, b) if x² - y = a²-b. Part (a): Prove that T is an equivalence relation on RX R. Part (b): Sketch the equivalence class of (2,1) (this will be a curve in the plane).
Transcribed Image Text:Problem 2 Let T be the relation on R x R defined by (x, y) T (a, b) if x² - y = a²-b. Part (a): Prove that T is an equivalence relation on RX R. Part (b): Sketch the equivalence class of (2,1) (this will be a curve in the plane).
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