Consider the following premises. William is climbing a mountain if and only if William is making tea. Jessica is a writer if and only if William is fast. If William were fast, then William is climbing a mountain. William is not making tea. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not a writer.
 From the fact that William is climbing a mountain if and only if William is making tea, and that William is not making tea we can infer that William is not climbing a mountain via biconditional elimination. From the fact that if William were fast, then William is climbing a mountain, and that William is not climbing a mountain we can infer that William is not fast via modus tollens. Finally, from the fact that Jessica is a writer if and only if William is fast, and that William is not fast we can infer that Jessica is not a writer via biconditional elimination. Therefore, the answer is yes.