Consider the following premises. For all z, if z were a sailor, then z is a taxi driver. For all z, if z were a taxi driver, then z is a sailor. There is at least one z for which if z were a sailor, then z is a taxi driver. Can we infer the following from them? For all z, if is not true that z is a taxi driver if and only if z is a sailor.
 From the fact that there is at least one z for which if z were a sailor, then z is a taxi driver, and that for all z, if z were a taxi driver, then z is a sailor we can infer that there is at least one z for which z is a sailor if and only if z is a taxi driver. From the fact that there is at least one z for which z is a sailor if and only if z is a taxi driver we can infer that there is at least one z for which if z were a taxi driver, then z is a sailor. Finally, from the fact that there is at least one z for which if z were a taxi driver, then z is a sailor, and that for all z, if z were a sailor, then z is a taxi driver we can infer that there is at least one z for which z is a taxi driver if and only if z is a sailor, which contradicts that For all z, if is not true that z is a taxi driver if and only if z is a sailor. Therefore, the answer is no.