Consider the following premises. If it is sunny, then it is snowing. Jennifer is a nurse if and only if it is overcast. If Richard were a carpenter, then it is snowing. It is sunny or Richard is a carpenter. If it is overcast, then it is not snowing. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is a nurse.
 From the fact that if it is sunny, then it is snowing, that if Richard were a carpenter, then it is snowing, and that it is sunny or Richard is a carpenter we can infer that it is snowing via disjunction elimination. From the fact that if it is overcast, then it is not snowing, and that it is snowing we can infer that it is not overcast via modus tollens. Finally, from the fact that Jennifer is a nurse if and only if it is overcast, and that it is not overcast we can infer that Jennifer is not a nurse via biconditional elimination, which contradicts that Jennifer is a nurse. Therefore, the answer is no.