Consider the following premises. For all x_7, x_7 is not a carpenter. For all x_7, x_7 is a carpenter if and only if x_7 will work. For all x_7, x_7 will work or x_7 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: Richard is a soldier.
 From the fact that for all x_7, x_7 is a carpenter if and only if x_7 will work, and that for all x_7, x_7 is not a carpenter we can infer that for all x_7, x_7 will not work via universal biconditional elimination. From the fact that for all x_7, x_7 will work or x_7 is a soldier, and that for all x_7, x_7 will not work we can infer that for all x_7, x_7 is a soldier via universal disjunctive syllogism. Finally, from the fact that for all x_7, x_7 is a soldier we can infer that Richard is a soldier via universal instantiation. Therefore, the answer is yes.