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Equivalence Relation Assignment | Assignment Help Services

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uestion: Which of the following is an equivalence relation? Give a proof for the one that is an equivalence relation. For the others, clearly explain why they are not. (i) The relation ∼ on Z defined by a∼b iff a2 +b2 ≤ 7. (ii) The relation ∼ in Z defined by a ∼ b iff a + b ≡ 0 (mod 5). (iii) The relation ∼ in Z defined by a ∼ b iff a2 + b2 = 0. (iv) The relation ∼ in Z defined by a ∼ b iff a + 2b ≡ 0 (mod 3). Please show all your steps in your logic. Thank you!

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