Consider the following premises. For all x_8, if x_8 plays squash, then x_8 is not driving a car. For all x_8, x_8 will drive a car if and only if x_8 will cook. For all x_8, x_8 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will play squash.
 From the fact that for all x_8, x_8 will drive a car if and only if x_8 will cook we can infer that for all x_8, if x_8 cooks, then x_8 is driving a car via universal biconditional elimination. From the fact that for all x_8, if x_8 cooks, then x_8 is driving a car, and that for all x_8, x_8 will cook we can infer that for all x_8, x_8 will drive a car via universal modus ponens. Finally, from the fact that for all x_8, if x_8 plays squash, then x_8 is not driving a car, and that for all x_8, x_8 will drive a car we can infer that for all x_8, x_8 will not play squash via universal modus tollens, which contradicts that There is at least one x_8 for which x_8 will play squash. Therefore, the answer is no.