Consider the following premises. There is at least one x_7 for which if x_7 were a nurse, then x_7 is poor. For all x_7, x_7 is not poor. For all x_7, if x_7 were poor, then x_7 is a nurse. Can we infer the following from them? There is at least one x_7 for which x_7 is not a nurse.
 From the fact that for all x_7, if x_7 were poor, then x_7 is a nurse, and that there is at least one x_7 for which if x_7 were a nurse, then x_7 is poor we can infer that there is at least one x_7 for which x_7 is poor if and only if x_7 is a nurse. From the fact that there is at least one x_7 for which x_7 is poor if and only if x_7 is a nurse we can infer that there is at least one x_7 for which if x_7 were a nurse, then x_7 is poor. Finally, from the fact that there is at least one x_7 for which if x_7 were a nurse, then x_7 is poor, and that for all x_7, x_7 is not poor we can infer that there is at least one x_7 for which x_7 is not a nurse. Therefore, the answer is yes.