Consider the following premises. Patricia is a nurse if and only if Barbara is a bartender. If Elisabeth were a sailor, then Patricia is a nurse. It is sunny or Barbara is not a bartender. It is not sunny. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not a sailor.
 From the fact that it is sunny or Barbara is not a bartender we can infer that if Barbara were a bartender, then it is sunny via rewriting. From the fact that if Barbara were a bartender, then it is sunny, and that it is not sunny we can infer that Barbara is not a bartender via modus tollens. From the fact that Patricia is a nurse if and only if Barbara is a bartender, and that Barbara is not a bartender we can infer that Patricia is not a nurse via biconditional elimination. Finally, from the fact that if Elisabeth were a sailor, then Patricia is a nurse, and that Patricia is not a nurse we can infer that Elisabeth is not a sailor via modus tollens. Therefore, the answer is yes.