Consider the following premises. Richard is not drinking water. Richard is fast or James is driving a car. For all x_10, if x_10 were fast, then x_10 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: James is driving a car.
 From the fact that for all x_10, if x_10 were fast, then x_10 is drinking water we can infer that if Richard were fast, then Richard is drinking water via universal instantiation. From the fact that if Richard were fast, then Richard is drinking water, and that Richard is not drinking water we can infer that Richard is not fast via modus tollens. Finally, from the fact that Richard is fast or James is driving a car, and that Richard is not fast we can infer that James is driving a car via disjunctive syllogism. Therefore, the answer is yes.