Consider the following premises. If it is late, then James is not sleeping. Richard is playing squash or James is sleeping. Richard is not playing squash. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that Richard is playing squash or James is sleeping, and that Richard is not playing squash we can infer that James is sleeping via disjunctive syllogism. Finally, from the fact that if it is late, then James is not sleeping, and that James is sleeping we can infer that it is not late via modus tollens, which contradicts that It is late. Therefore, the answer is no.