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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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.
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