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