Consider the following premises. Barbara is a scientist if and only if Charles is cooking. If Charles doesn't cook, then Patricia is a server. Barbara is not a scientist. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not a server.
 From the fact that Barbara is a scientist if and only if Charles is cooking we can infer that if Charles cooks, then Barbara is a scientist via biconditional elimination. From the fact that if Charles cooks, then Barbara is a scientist, and that Barbara is not a scientist we can infer that Charles is not cooking via modus tollens. Finally, from the fact that if Charles doesn't cook, then Patricia is a server, and that Charles is not cooking we can infer that Patricia is a server via modus ponens, which contradicts that Patricia is not a server. Therefore, the answer is no.