Consider the following premises. For all z, if z were a bartender, then z is a nurse. For all x, x is a nurse. For all z, if z were a nurse, then z is a bartender. Can we infer the following from them? William is not a bartender.
 From the fact that for all z, if z were a nurse, then z is a bartender, and that for all z, if z were a bartender, then z is a nurse we can infer that for all z, z is a nurse if and only if z is a bartender. From the fact that for all x, x is a nurse we can infer that William is a nurse. From the fact that for all z, z is a nurse if and only if z is a bartender we can infer that William is a nurse if and only if William is a bartender. From the fact that William is a nurse if and only if William is a bartender we can infer that if William were a nurse, then William is a bartender. Finally, from the fact that if William were a nurse, then William is a bartender, and that William is a nurse we can infer that William is a bartender, which contradicts that William is not a bartender. Therefore, the answer is no.