Consider the following premises. For all x_2, x_2 will work or x_2 is a mechanic. For all x_2, x_2 will not work. For all x_2, if x_2 were rich, then x_2 is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 is rich.
 From the fact that for all x_2, x_2 will work or x_2 is a mechanic, and that for all x_2, x_2 will not work we can infer that for all x_2, x_2 is a mechanic via universal disjunctive syllogism. Finally, from the fact that for all x_2, if x_2 were rich, then x_2 is not a mechanic, and that for all x_2, x_2 is a mechanic we can infer that for all x_2, x_2 is not rich via universal modus tollens, which contradicts that There is at least one x_2 for which x_2 is rich. Therefore, the answer is no.