Consider the following premises. For all x_7, if x_7 were a nurse, then x_7 is sleeping. For all x_7, x_7 is a nurse and x_7 is a politician. For all x_7, x_7 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will sleep and x_7 is a sailor.
 From the fact that for all x_7, x_7 is a nurse and x_7 is a politician we can infer that for all x_7, x_7 is a nurse via universal simplification. From the fact that for all x_7, if x_7 were a nurse, then x_7 is sleeping, and that for all x_7, x_7 is a nurse we can infer that for all x_7, x_7 will sleep via universal modus ponens. Finally, from the fact that for all x_7, x_7 will sleep, and that for all x_7, x_7 is a sailor we can infer that for all x_7, x_7 will sleep and x_7 is a sailor via universal conjunction. Therefore, the answer is yes.