(a) Prove that the sum and product of abstract symbols is well-defined. That is, if [a1, b1] = [a2, b2] and [c1, d1] = [c2, d2], prove that we have [a1, b1] · [c1, d1] = [a2, b2] · [c2, d2] and [a1, b1] + [c1, d1] = [a2, b2] + [c2, d2] . (b) One can check that Q satisfies all of the axioms of Z except for the Well-Ordering Axiom (please don’t check this), with additive identity [0, 1] ∈ Q and m...