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