Consider the following premises. For all x_8, x_8 will not make tea. For all x_8, if x_8 plays squash, then x_8 is making tea. For all x_8, x_8 will play squash if and only if x_8 will play tennis. 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 tennis.
 From the fact that for all x_8, x_8 will play squash if and only if x_8 will play tennis we can infer that for all x_8, if x_8 plays tennis, then x_8 is playing squash via universal biconditional elimination. From the fact that for all x_8, if x_8 plays squash, then x_8 is making tea, and that for all x_8, x_8 will not make tea we can infer that for all x_8, x_8 will not play squash via universal modus tollens. Finally, from the fact that for all x_8, if x_8 plays tennis, then x_8 is playing squash, and that for all x_8, x_8 will not play squash we can infer that for all x_8, x_8 will not play tennis via universal modus tollens, which contradicts that There is at least one x_8 for which x_8 will play tennis. Therefore, the answer is no.