Consider the following premises. Patricia is not a bartender. If it is overcast, then Patricia is listening to a song. It is overcast if and only if Thomas is running. Patricia is listening to a song if and only if Patricia is a bartender. Can we infer the following from them? If we can, name the inference rule being used: Thomas is running.
 From the fact that Patricia is listening to a song if and only if Patricia is a bartender, and that Patricia is not a bartender we can infer that Patricia is not listening to a song via biconditional elimination. From the fact that if it is overcast, then Patricia is listening to a song, and that Patricia is not listening to a song we can infer that it is not overcast via modus tollens. Finally, from the fact that it is overcast if and only if Thomas is running, and that it is not overcast we can infer that Thomas is not running via biconditional elimination, which contradicts that Thomas is running. Therefore, the answer is no.