by xRy if and only if 7 divides x² – yʻ.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Proficiency #18. [Equivalence Relations]
Let A = Z, and let the relation R be defined on A by r Ry if and only if 7 divides a² – y².
(a) Show that R is an equivalence relation.
(b) List three elements in [3]R, the equivalence class of 3 under R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79fec644-cc9a-4e79-932f-9a07bdd10b3d%2F4f5c9dbe-7438-4064-97b3-d44c5001be4a%2Fcn3ps5j_processed.png&w=3840&q=75)
Transcribed Image Text:Proficiency #18. [Equivalence Relations]
Let A = Z, and let the relation R be defined on A by r Ry if and only if 7 divides a² – y².
(a) Show that R is an equivalence relation.
(b) List three elements in [3]R, the equivalence class of 3 under R.
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