Consider the following premises. If Karen climbs a mountain, then it is raining. If Linda were a janitor, then Jennifer is running. Jennifer is not running. Linda is a janitor if and only if it is raining. If it rains, then Karen is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: Karen is climbing a mountain.
 From the fact that if it rains, then Karen is climbing a mountain, and that if Karen climbs a mountain, then it is raining we can infer that it is raining if and only if Karen is climbing a mountain via biconditional introduction. From the fact that if Linda were a janitor, then Jennifer is running, and that Jennifer is not running we can infer that Linda is not a janitor via modus tollens. From the fact that Linda is a janitor if and only if it is raining, and that Linda is not a janitor we can infer that it is not raining via biconditional elimination. Finally, from the fact that it is raining if and only if Karen is climbing a mountain, and that it is not raining we can infer that Karen is not climbing a mountain via biconditional elimination, which contradicts that Karen is climbing a mountain. Therefore, the answer is no.