Consider the following premises. For all z_4, z_4 is a nurse if and only if z_4 will work. For all z_4, z_4 is a nurse or z_4 will not play a game. Can we infer the following from them? There is at least one z_4 for which the fact that z_4 plays a game does not imply that z_4 is working.
 From the fact that for all z_4, z_4 is a nurse or z_4 will not play a game we can infer that for all z_4, if z_4 plays a game, then z_4 is a nurse. From the fact that for all z_4, z_4 is a nurse if and only if z_4 will work we can infer that for all z_4, if z_4 were a nurse, then z_4 is working. Finally, from the fact that for all z_4, if z_4 plays a game, then z_4 is a nurse, and that for all z_4, if z_4 were a nurse, then z_4 is working we can infer that for all z_4, if z_4 plays a game, then z_4 is working, which contradicts that There is at least one z_4 for which the fact that z_4 plays a game does not imply that z_4 is working. Therefore, the answer is no.