Consider the following premises. If it is not sunny, then Karen is climbing a mountain. William is not playing tennis. It is sunny if and only if William is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: Karen is not climbing a mountain.
 From the fact that it is sunny if and only if William is playing tennis, and that William is not playing tennis we can infer that it is not sunny via biconditional elimination. Finally, from the fact that if it is not sunny, then Karen is climbing a mountain, and that it is not sunny we can infer that Karen is climbing a mountain via modus ponens, which contradicts that Karen is not climbing a mountain. Therefore, the answer is no.