Consider the following premises. James is listening to a song. If Linda writes a letter, then Susan is not a janitor. If it is late, then Linda is writing a letter. If James listens to a song, then it is late. Susan is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Charles is playing tennis.
 From the fact that if Linda writes a letter, then Susan is not a janitor, and that Susan is a janitor we can infer that Linda is not writing a letter via modus tollens. From the fact that if it is late, then Linda is writing a letter, and that Linda is not writing a letter we can infer that it is not late via modus tollens. From the fact that James is listening to a song we can infer that James is listening to a song or Charles is playing tennis via addition. From the fact that if James listens to a song, then it is late, and that it is not late we can infer that James is not listening to a song via modus tollens. Finally, from the fact that James is listening to a song or Charles is playing tennis, and that James is not listening to a song we can infer that Charles is playing tennis via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.