Consider the following premises. If Michael were a cashier, then James is cooking. For all x_10, if x_10 cooks, then x_10 is poor. If James were poor, then Michael is a cashier. Can we infer the following from them? James is cooking if and only if James is poor.
 From the fact that for all x_10, if x_10 cooks, then x_10 is poor we can infer that if James cooks, then James is poor. From the fact that if James were poor, then Michael is a cashier, and that if Michael were a cashier, then James is cooking we can infer that if James were poor, then James is cooking. Finally, from the fact that if James cooks, then James is poor, and that if James were poor, then James is cooking we can infer that James is cooking if and only if James is poor. Therefore, the answer is yes.