Consider the following premises. For all z_4, if z_4 were a nurse, then z_4 is driving a car. For all z_4, if z_4 drives a car, then z_4 is a nurse. For all z_4, z_4 will not drive a car. Can we infer the following from them? There is at least one z_4 for which z_4 is a nurse.
 From the fact that for all z_4, if z_4 drives a car, then z_4 is a nurse, and that for all z_4, if z_4 were a nurse, then z_4 is driving a car we can infer that for all z_4, z_4 will drive a car if and only if z_4 is a nurse. From the fact that for all z_4, z_4 will drive a car if and only if z_4 is a nurse we can infer that for all z_4, if z_4 were a nurse, then z_4 is driving a car. Finally, from the fact that for all z_4, if z_4 were a nurse, then z_4 is driving a car, and that for all z_4, z_4 will not drive a car we can infer that for all z_4, z_4 is not a nurse, which contradicts that There is at least one z_4 for which z_4 is a nurse. Therefore, the answer is no.