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9. For a, b E R, define a~b if and only if a - b E Z. Prove that defines an equivalence relation on Z.

9. For a, b E R, define a~b if and only if a - b E Z. Prove that defines an equivalence relation on Z.

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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9. For a, b E R, define a~b if and only if a - b E Z. Prove that defines an equivalence relation on Z. 2
Transcribed Image Text:9. For a, b E R, define a~b if and only if a - b E Z. Prove that defines an equivalence relation on Z. 2
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