Consider the following premises. For all x_1, x_1 is not an electrician. For all x_1, if x_1 were a nurse, then x_1 is an electrician. For all x_1, if x_1 were a poet, then x_1 is a nurse. Sarah is a poet or it is overcast. Can we infer the following from them? If we can, name the inference rule being used: It is overcast.
 From the fact that for all x_1, if x_1 were a poet, then x_1 is a nurse, and that for all x_1, if x_1 were a nurse, then x_1 is an electrician we can infer that for all x_1, if x_1 were a poet, then x_1 is an electrician via universal transitivity. From the fact that for all x_1, if x_1 were a poet, then x_1 is an electrician, and that for all x_1, x_1 is not an electrician we can infer that for all x_1, x_1 is not a poet via universal modus tollens. From the fact that for all x_1, x_1 is not a poet we can infer that Sarah is not a poet via universal instantiation. Finally, from the fact that Sarah is a poet or it is overcast, and that Sarah is not a poet we can infer that it is overcast via disjunctive syllogism. Therefore, the answer is yes.