Consider the following premises. For all x_2, x_2 is a lawyer or x_2 is a bartender. For all x_2, if x_2 were a bartender, then x_2 is cooking. For all x_2, x_2 will cook or x_2 is not a lawyer. Can we infer the following from them? For all x_2, x_2 will cook.
 From the fact that for all x_2, x_2 will cook or x_2 is not a lawyer we can infer that for all x_2, if x_2 were a lawyer, then x_2 is cooking. Finally, from the fact that for all x_2, if x_2 were a lawyer, then x_2 is cooking, that for all x_2, if x_2 were a bartender, then x_2 is cooking, and that for all x_2, x_2 is a lawyer or x_2 is a bartender we can infer that for all x_2, x_2 will cook. Therefore, the answer is yes.