Consider the following premises. There is at least one x_6 for which x_6 is sad if and only if x_6 will cook. For all x_6, x_6 is not a politician. For all x_6, if x_6 cooks, then x_6 is a politician. Can we infer the following from them? For all x_6, x_6 is sad.
 From the fact that for all x_6, if x_6 cooks, then x_6 is a politician, and that for all x_6, x_6 is not a politician we can infer that for all x_6, x_6 will not cook. From the fact that there is at least one x_6 for which x_6 is sad if and only if x_6 will cook we can infer that there is at least one x_6 for which if x_6 were sad, then x_6 is cooking. Finally, from the fact that there is at least one x_6 for which if x_6 were sad, then x_6 is cooking, and that for all x_6, x_6 will not cook we can infer that there is at least one x_6 for which x_6 is not sad, which contradicts that For all x_6, x_6 is sad. Therefore, the answer is no.