The answer is clear with writing Let S Z For each positive

The answer is clear with writing

Let S = Z. For each positive integer m. we define the modular relation ( _m) by x _m y Iff m|(x - y) or x _m y iff x and y have the same remainder when divided by m. Examples: 7 _5 2, 6 _3 9, 10 _5 0, -12 _5 3. - 12 _3 0. For any natural number m Show that the modular relation ( _m ) is an equivalence relation on Z. If it\'s an equivalence relation then consider the modular relation ( _2) and find the equivalence class of E_1 (or [1]).

Solution