Consider the following premises. Barbara is an artist if and only if Jessica is a soldier. William is not happy. William is happy if and only if Barbara is an artist. If Jessica were not a soldier, then James is a janitor. Can we infer the following from them? If we can, name the inference rule being used: James is not a janitor.
 From the fact that William is happy if and only if Barbara is an artist we can infer that if Barbara were an artist, then William is happy via biconditional elimination. From the fact that if Barbara were an artist, then William is happy, and that William is not happy we can infer that Barbara is not an artist via modus tollens. From the fact that Barbara is an artist if and only if Jessica is a soldier, and that Barbara is not an artist we can infer that Jessica is not a soldier via biconditional elimination. Finally, from the fact that if Jessica were not a soldier, then James is a janitor, and that Jessica is not a soldier we can infer that James is a janitor via modus ponens, which contradicts that James is not a janitor. Therefore, the answer is no.