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For points (x, y) and (u, v) in the set R?, define (x, y) ~ (u, v) if and only if r – y = u – v. (a) Prove that ~ defines an equivalence relation on R². (b) Compute the equivalence class of the point (0, 4). The collection of points in this class deter mines a common geometric object in R2. Describe it.

For points (x, y) and (u, v) in the set R?, define (x, y) ~ (u, v) if and only if r – y = u – v. (a) Prove that ~ defines an equivalence relation on R². (b) Compute the equivalence class of the point (0, 4). The collection of points in this class deter mines a common geometric object in R2. Describe it.

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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5. For points (x, y) and (u, v) in the set R?, define (x, y) ~ (u, v) if and only if r – y = u – v. (a) Prove that ~ defines an equivalence relation on R². (b) Compute the equivalence class of the point (0, 4). The collection of points in this class deter- mines a common geometric object in R?. Describe it.
Transcribed Image Text:5. For points (x, y) and (u, v) in the set R?, define (x, y) ~ (u, v) if and only if r – y = u – v. (a) Prove that ~ defines an equivalence relation on R². (b) Compute the equivalence class of the point (0, 4). The collection of points in this class deter- mines a common geometric object in R?. Describe it.
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