2 In lectures, we gave a construction for the rational numbers. This started by looking at the set S of all pairs of the form (a, b), with a, b E Z and b = O, and then considering the relation Q on S = Z X (Z \\ {0}) defined by: (a,b)Q(c,d] ifand only if ad = bc. Explain why things would go badly wrong if we allow 8 to include pairs (91,19) with b = O: that is, if we defined a new relation R on Z X Z by: (a,b)R(c,d) if and only if ad =bc. (Hint: the answer does not involve rdivision by zero'.)