Consider the following premises. For all x_5, x_5 will not take a plane. For all x_5, x_5 is a janitor or x_5 will sleep. For all x_5, if x_5 were a janitor, then x_5 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will sleep or x_5 will cook.
 From the fact that for all x_5, if x_5 were a janitor, then x_5 is taking a plane, and that for all x_5, x_5 will not take a plane we can infer that for all x_5, x_5 is not a janitor via universal modus tollens. From the fact that for all x_5, x_5 is a janitor or x_5 will sleep, and that for all x_5, x_5 is not a janitor we can infer that for all x_5, x_5 will sleep via universal disjunctive syllogism. Finally, from the fact that for all x_5, x_5 will sleep we can infer that for all x_5, x_5 will sleep or x_5 will cook via universal addition. Therefore, the answer is yes.