Consider the following premises. For all x_15, x_15 is a janitor or x_15 is an astronaut. For all x_15, if x_15 were an astronaut, then x_15 is an electrician. For all x_15, x_15 is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is an electrician or Karen is an office clerk.
 From the fact that for all x_15, x_15 is a janitor or x_15 is an astronaut, and that for all x_15, x_15 is not a janitor we can infer that for all x_15, x_15 is an astronaut via universal disjunctive syllogism. From the fact that for all x_15, if x_15 were an astronaut, then x_15 is an electrician, and that for all x_15, x_15 is an astronaut we can infer that for all x_15, x_15 is an electrician via universal modus ponens. From the fact that for all x_15, x_15 is an electrician we can infer that Jennifer is an electrician via universal instantiation. Finally, from the fact that Jennifer is an electrician we can infer that Jennifer is an electrician or Karen is an office clerk via addition. Therefore, the answer is yes.