Consider the following premises. For all x, x is bored or x is a janitor. For all x, if x were bored, then x is writing a letter. For all x, x will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not a janitor.
 From the fact that for all x, if x were bored, then x is writing a letter, and that for all x, x will not write a letter we can infer that for all x, x is not bored via universal modus tollens. Finally, from the fact that for all x, x is bored or x is a janitor, and that for all x, x is not bored we can infer that for all x, x is a janitor via universal disjunctive syllogism, which contradicts that Elisabeth is not a janitor. Therefore, the answer is no.