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