Prove that the completeness and/or transitivity axioms (page 519), imply the following statements. What axiom(s) do your proofs rely on?

(a) o2  o1 is equivalent to o1 ! o2

(b) if o1 ! o2 and o2 ! o3 then o1 ! o3

(c) if o1 ! o2 and o2 o3 then o1 ! o3

(d) if o1 o2 and o2 o3 then o1 o3.