Consider the following premises. For all x_5, x_5 will cook or x_5 will make tea. For all x_5, if x_5 plays squash, then x_5 is not making tea. There is at least one x_5 for which x_5 will not cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not play squash.
 From the fact that for all x_5, x_5 will cook or x_5 will make tea, and that there is at least one x_5 for which x_5 will not cook we can infer that there is at least one x_5 for which x_5 will make tea via existential disjunctive syllogism. Finally, from the fact that for all x_5, if x_5 plays squash, then x_5 is not making tea, and that there is at least one x_5 for which x_5 will make tea we can infer that there is at least one x_5 for which x_5 will not play squash via existential modus tollens. Therefore, the answer is yes.