Consider the following premises. For all x_10, x_10 will not drink water. For all x_10, if x_10 drinks water, then x_10 is a bartender. If it is late, then Jennifer is a bartender. For all x_10, if x_10 were a bartender, then x_10 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that for all x_10, if x_10 were a bartender, then x_10 is drinking water, and that for all x_10, if x_10 drinks water, then x_10 is a bartender we can infer that for all x_10, x_10 is a bartender if and only if x_10 will drink water via universal biconditional introduction. From the fact that for all x_10, x_10 is a bartender if and only if x_10 will drink water, and that for all x_10, x_10 will not drink water we can infer that for all x_10, x_10 is not a bartender via universal biconditional elimination. From the fact that for all x_10, x_10 is not a bartender we can infer that Jennifer is not a bartender via universal instantiation. Finally, from the fact that if it is late, then Jennifer is a bartender, and that Jennifer is not a bartender we can infer that it is not late via modus tollens, which contradicts that It is late. Therefore, the answer is no.