It does not imply one to one or onto. Unique pair (a, b) only implies for any a, the corresponding b is unambiguous. There could easily be (a1, b) and (a2, b)

It does not imply one to one or onto. Unique pair (a, b) only implies for any a, the corresponding b is unambiguous. There could easily be (a1, b) and (a2, b), thus not one to one, and there could easily be a b1 such that there is no corresponding A, thus not onto.