Please show the following question in detail: " Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x + 2y). (a) Prove that R is an equivalence relation. (b) If S = {−7, −6, −2, 0, 1, 4, 5, 7}, then what are the distinct equivalence classes in this

Please show the following question in detail: " Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x + 2y). (a) Prove that R is an equivalence relation. (b) If S = {−7, −6, −2, 0, 1, 4, 5, 7}, then what are the distinct equivalence classes in this

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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Question

Please show the following question in detail: " Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x + 2y).
(a) Prove that R is an equivalence relation.
(b) If S = {−7, −6, −2, 0, 1, 4, 5, 7}, then what are the distinct equivalence classes in this case?"

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Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x + 2y). If S = {−7, −6, −2, 0, 1, 4, 5, 7}, then what are the distinct equivalence classes in this case? Please show how you find them
please answer me asap with answer