Consider the following premises. Michael is cooking or Karen is a taxi driver. For all x_10, if x_10 cooks, then x_10 is a mechanic. Michael is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: Karen is a taxi driver.
 From the fact that for all x_10, if x_10 cooks, then x_10 is a mechanic we can infer that if Michael cooks, then Michael is a mechanic via universal instantiation. From the fact that if Michael cooks, then Michael is a mechanic, and that Michael is not a mechanic we can infer that Michael is not cooking via modus tollens. Finally, from the fact that Michael is cooking or Karen is a taxi driver, and that Michael is not cooking we can infer that Karen is a taxi driver via disjunctive syllogism. Therefore, the answer is yes.