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