Consider the following premises. For all x_12, if x_12 climbs a mountain, then x_12 is not a scientist. Patricia is a janitor if and only if Sarah is climbing a mountain. For all x_12, x_12 is a scientist. If Linda were a mechanic, then Patricia is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Linda is not a mechanic.
 From the fact that for all x_12, if x_12 climbs a mountain, then x_12 is not a scientist, and that for all x_12, x_12 is a scientist we can infer that for all x_12, x_12 will not climb a mountain via universal modus tollens. From the fact that for all x_12, x_12 will not climb a mountain we can infer that Sarah is not climbing a mountain via universal instantiation. From the fact that Patricia is a janitor if and only if Sarah is climbing a mountain, and that Sarah is not climbing a mountain we can infer that Patricia is not a janitor via biconditional elimination. Finally, from the fact that if Linda were a mechanic, then Patricia is a janitor, and that Patricia is not a janitor we can infer that Linda is not a mechanic via modus tollens. Therefore, the answer is yes.