Let S = Z x (Z – {0}) = {(a, b) E Z²: b+ 0}. Define an equivalence relation on S by: (a, b) ~ (c, d) if and only if ad – bc 0. (a) Show that ~ is an equivalence relation on S. (b) Describe the...

Extracted text: Let S = Z x (Z – {0}) = {(a, b) E Z²: b+ 0}. Define an equivalence relation on S by: (a, b) ~ (c, d) if and only if ad – bc 0. (a) Show that ~ is an equivalence relation on S. (b) Describe the equivalence classes of - (as sets, in set building notation). (c) Show that the function 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?