Consider the following premises. Barbara is sleeping. If Richard were a lawyer, then Barbara is not sleeping. Susan is an astronaut or James is writing a letter. If Susan were an astronaut, then Richard is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: James is not writing a letter.
 From the fact that if Richard were a lawyer, then Barbara is not sleeping, and that Barbara is sleeping we can infer that Richard is not a lawyer via modus tollens. From the fact that if Susan were an astronaut, then Richard is a lawyer, and that Richard is not a lawyer we can infer that Susan is not an astronaut via modus tollens. Finally, from the fact that Susan is an astronaut or James is writing a letter, and that Susan is not an astronaut we can infer that James is writing a letter via disjunctive syllogism, which contradicts that James is not writing a letter. Therefore, the answer is no.