Question 5. Let ~ be the equivalence relation defined on Z by x~ y 3 divides (xy) For each x ЄZ, 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 is well-defined. x-y=xy (ii) Determine whether the exponentiation operation on Z/ is well-defined. [x][y] = [x] ~ given by

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