Consider the following premises. If Mary were bored, then John is a doctor. If Sarah goes running, then Mary is bored. If John were a doctor, then Robert is a janitor. Robert is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: Sarah is not running.
 From the fact that if John were a doctor, then Robert is a janitor, and that Robert is not a janitor we can infer that John is not a doctor via modus tollens. From the fact that if Mary were bored, then John is a doctor, and that John is not a doctor we can infer that Mary is not bored via modus tollens. Finally, from the fact that if Sarah goes running, then Mary is bored, and that Mary is not bored we can infer that Sarah is not running via modus tollens. Therefore, the answer is yes.