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

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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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