Question 5. Let ~ be the equivalence relation defined on Z by x~ Y 3 divides (xy) For each x Z, let [x] be the ~-equivalence class which contains x; and let Z/~ be the set of ~-equivalence classes. 1 2 361 PRACTICE FIRST MIDTERM QUESTIONS 2024 (i) Prove that the multiplication operation on Z/ ~ given by x-y=xy is well-defined. (ii) Determine whether the exponentiation operation on Z/ ~ given by [x][v] = [x] is well-defined.

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