Consider the following premises. If Barbara were a doctor, then Patricia is a janitor. If Patricia were a janitor, then Barbara is a doctor. William is not an electrician. William is an electrician if and only if Patricia is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a doctor.
 From the fact that William is an electrician if and only if Patricia is a janitor, and that William is not an electrician we can infer that Patricia is not a janitor via biconditional elimination. From the fact that if Patricia were a janitor, then Barbara is a doctor, and that if Barbara were a doctor, then Patricia is a janitor we can infer that Patricia is a janitor if and only if Barbara is a doctor via biconditional introduction. Finally, from the fact that Patricia is a janitor if and only if Barbara is a doctor, and that Patricia is not a janitor we can infer that Barbara is not a doctor via biconditional elimination, which contradicts that Barbara is a doctor. Therefore, the answer is no.