2. Recall that the set Q of rational numbers consists of
equivalence classes of elements of Z × Z\{0} under the equivalence
relation 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 definition
of multiplication of elements of Q makes sense (i.e. is
“well-defined”): [a, b] · [r, s] = [ar, bs]. (Recall this...