Consider the following premises. Linda is not driving a car. It is overcast if and only if Linda is driving a car. If it is not overcast, then Jennifer is a writer. If Joseph were a carpenter, then Jennifer is not a writer. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not a carpenter.
 From the fact that it is overcast if and only if Linda is driving a car, and that Linda is not driving a car we can infer that it is not overcast via biconditional elimination. From the fact that if it is not overcast, then Jennifer is a writer, and that it is not overcast we can infer that Jennifer is a writer via modus ponens. Finally, from the fact that if Joseph were a carpenter, then Jennifer is not a writer, and that Jennifer is a writer we can infer that Joseph is not a carpenter via modus tollens. Therefore, the answer is yes.