Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈ X, let xRy if and only if x^2 - y^2 or x^2 + y^2 is divisible by 10. Prove that R is an equivalence relation and determine the equivalence classes of R.

Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈ X, let xRy if and only if x^2 - y^2 or x^2 + y^2 is divisible by 10. Prove that R is an equivalence relation and determine the equivalence classes of 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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