Consider the following premises. David is working or Patricia is an artist. It is late or Patricia is not an artist. David is not working. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that David is working or Patricia is an artist, and that David is not working we can infer that Patricia is an artist via disjunctive syllogism. From the fact that it is late or Patricia is not an artist we can infer that if Patricia were an artist, then it is late via rewriting. Finally, from the fact that if Patricia were an artist, then it is late, and that Patricia is an artist we can infer that it is late via modus ponens. Therefore, the answer is yes.