Consider the following premises. There is at least one x_6 for which x_6 will read a book. For all x_6, x_6 will drive a car. For all x_6, if x_6 were a scientist, then x_6 is not driving a car. For all x_6, x_6 is a scientist or x_6 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will read a book and x_6 is a bartender.
 From the fact that for all x_6, if x_6 were a scientist, then x_6 is not driving a car, and that for all x_6, x_6 will drive a car we can infer that for all x_6, x_6 is not a scientist via universal modus tollens. From the fact that for all x_6, x_6 is a scientist or x_6 is a bartender, and that for all x_6, x_6 is not a scientist we can infer that for all x_6, x_6 is a bartender via universal disjunctive syllogism. Finally, from the fact that there is at least one x_6 for which x_6 will read a book, and that for all x_6, x_6 is a bartender we can infer that there is at least one x_6 for which x_6 will read a book and x_6 is a bartender via existential conjunction. Therefore, the answer is yes.