Question: Which of the following is an equivalence relation?

Question: 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!