Consider the following premises. For all x_6, x_6 is a cashier or x_6 is poor. For all x_6, if x_6 were a cashier, then x_6 is not a nurse. For all x_6, x_6 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is poor or x_6 will work.
 From the fact that for all x_6, if x_6 were a cashier, then x_6 is not a nurse, and that for all x_6, x_6 is a nurse we can infer that for all x_6, x_6 is not a cashier via universal modus tollens. From the fact that for all x_6, x_6 is a cashier or x_6 is poor, and that for all x_6, x_6 is not a cashier we can infer that for all x_6, x_6 is poor via universal disjunctive syllogism. Finally, from the fact that for all x_6, x_6 is poor we can infer that for all x_6, x_6 is poor or x_6 will work via universal addition. Therefore, the answer is yes.