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