Consider the following premises. It is cloudy if and only if Joseph is poor. Robert is a janitor or Joseph is poor. It is not cloudy. Can we infer the following from them? If we can, name the inference rule being used: Robert is not a janitor.
 From the fact that it is cloudy if and only if Joseph is poor, and that it is not cloudy we can infer that Joseph is not poor via biconditional elimination. From the fact that Robert is a janitor or Joseph is poor we can infer that if Joseph were not poor, then Robert is a janitor via rewriting. Finally, from the fact that if Joseph were not poor, then Robert is a janitor, and that Joseph is not poor we can infer that Robert is a janitor via modus ponens, which contradicts that Robert is not a janitor. Therefore, the answer is no.