2. Recall that the set Q of rational numbers consists ofequivalence classes of elements of Z × Z{0} under the equivalencerelation R defined by: (a, b)R(c, d) ?? ad = bc. We write [a, b]for the equivalence class of the element (a, b). Using this setup,do the following problems: 2A. Show that the following definitionof multiplication of elements of Q makes sense (i.e. is“well-defined”): [a, b] · [r, s] = [ar, bs]. (Recall this meansthat we must check that the definition gives the same answer nomatter which representative of the equivalence class we use tocompute the product.) [This is the same as problem 19 of section4.2.]
