Consider the following premises. For all z, z is a bartender or z is an office clerk. For all z, z is a bartender if and only if z is poor. For all z, z is not poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is not an office clerk.
 From the fact that for all z, z is a bartender if and only if z is poor we can infer that for all z, if z were a bartender, then z is poor via universal biconditional elimination. From the fact that for all z, if z were a bartender, then z is poor, and that for all z, z is not poor we can infer that for all z, z is not a bartender via universal modus tollens. Finally, from the fact that for all z, z is a bartender or z is an office clerk, and that for all z, z is not a bartender we can infer that for all z, z is an office clerk via universal disjunctive syllogism, which contradicts that There is at least one z for which z is not an office clerk. Therefore, the answer is no.