Consider the following premises. If it is overcast, then James is a musician. James is not a musician. William is climbing a mountain if and only if Barbara is cooking. If Barbara cooks, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: William is not climbing a mountain.
 From the fact that if it is overcast, then James is a musician, and that James is not a musician we can infer that it is not overcast via modus tollens. From the fact that if Barbara cooks, then it is overcast, and that it is not overcast we can infer that Barbara is not cooking via modus tollens. Finally, from the fact that William is climbing a mountain if and only if Barbara is cooking, and that Barbara is not cooking we can infer that William is not climbing a mountain via biconditional elimination. Therefore, the answer is yes.