Consider the following premises. For all x_8, x_8 will not climb a mountain. Charles is fast or Karen is playing squash. For all x_8, x_8 will climb a mountain if and only if x_8 is fast. Can we infer the following from them? If we can, name the inference rule being used: Karen is playing squash.
 From the fact that for all x_8, x_8 will climb a mountain if and only if x_8 is fast, and that for all x_8, x_8 will not climb a mountain we can infer that for all x_8, x_8 is not fast via universal biconditional elimination. From the fact that for all x_8, x_8 is not fast we can infer that Charles is not fast via universal instantiation. Finally, from the fact that Charles is fast or Karen is playing squash, and that Charles is not fast we can infer that Karen is playing squash via disjunctive syllogism. Therefore, the answer is yes.