Consider the following premises. There is at least one x_8 for which x_8 will cook or x_8 is a writer. For all x_8, x_8 is not a soldier. For all x_8, x_8 is a soldier if and only if x_8 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is a writer.
 From the fact that for all x_8, x_8 is a soldier if and only if x_8 will cook we can infer that for all x_8, if x_8 cooks, then x_8 is a soldier via universal biconditional elimination. From the fact that for all x_8, if x_8 cooks, then x_8 is a soldier, and that for all x_8, x_8 is not a soldier we can infer that for all x_8, x_8 will not cook via universal modus tollens. Finally, from the fact that there is at least one x_8 for which x_8 will cook or x_8 is a writer, and that for all x_8, x_8 will not cook we can infer that there is at least one x_8 for which x_8 is a writer via existential disjunctive syllogism. Therefore, the answer is yes.