Consider the following premises. For all x_7, if x_7 were a politician, then x_7 is cooking. For all x_7, if x_7 cooks, then x_7 is a politician. For all x_7, if x_7 were a scientist, then x_7 is a politician. There is at least one x_7 for which if x_7 were a politician, then x_7 is a scientist. For all x_7, x_7 will not cook. Can we infer the following from them? There is at least one x_7 for which x_7 is not a scientist.
 From the fact that for all x_7, if x_7 cooks, then x_7 is a politician, and that for all x_7, if x_7 were a politician, then x_7 is cooking we can infer that for all x_7, x_7 will cook if and only if x_7 is a politician. From the fact that for all x_7, x_7 will cook if and only if x_7 is a politician, and that for all x_7, x_7 will not cook we can infer that for all x_7, x_7 is not a politician. From the fact that for all x_7, if x_7 were a scientist, then x_7 is a politician, and that there is at least one x_7 for which if x_7 were a politician, then x_7 is a scientist we can infer that there is at least one x_7 for which x_7 is a scientist if and only if x_7 is a politician. Finally, from the fact that there is at least one x_7 for which x_7 is a scientist if and only if x_7 is a politician, and that for all x_7, x_7 is not a politician we can infer that there is at least one x_7 for which x_7 is not a scientist. Therefore, the answer is yes.