Consider the following premises. For all x_4, x_4 will climb a mountain if and only if x_4 is a carpenter. Jennifer is not climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not a carpenter.
 From the fact that for all x_4, x_4 will climb a mountain if and only if x_4 is a carpenter we can infer that for all x_4, if x_4 were a carpenter, then x_4 is climbing a mountain via universal biconditional elimination. From the fact that for all x_4, if x_4 were a carpenter, then x_4 is climbing a mountain we can infer that if Jennifer were a carpenter, then Jennifer is climbing a mountain via universal instantiation. Finally, from the fact that if Jennifer were a carpenter, then Jennifer is climbing a mountain, and that Jennifer is not climbing a mountain we can infer that Jennifer is not a carpenter via modus tollens. Therefore, the answer is yes.