F U}. Deine an equivalence relation on S by: (a, b) ~ (c, d) if and only if ad – bc = 0. (a) Show that (b) Describe the equivalence classes of ~ (as sets, in set building notation). (c) Show that the function is an equivalence relation on S. а f: (S/ ~) → Q, [(a, b)] → is well defined, and also a bijection. d) Is the function g: (S/ ~) → Z, [(a,b)] → a well defined?

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