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