Consider the following premises. For all y_3, y_3 is a politician or y_3 will cook. For all y_3, y_3 is happy if and only if y_3 is a mechanic. For all y_3, y_3 is a politician if and only if y_3 is happy. For all y_3, y_3 is not a mechanic. Can we infer the following from them? For all y_3, y_3 will cook.
 From the fact that for all y_3, y_3 is happy if and only if y_3 is a mechanic, and that for all y_3, y_3 is not a mechanic we can infer that for all y_3, y_3 is not happy. From the fact that for all y_3, y_3 is a politician if and only if y_3 is happy we can infer that for all y_3, if y_3 were a politician, then y_3 is happy. From the fact that for all y_3, if y_3 were a politician, then y_3 is happy, and that for all y_3, y_3 is not happy we can infer that for all y_3, y_3 is not a politician. Finally, from the fact that for all y_3, y_3 is a politician or y_3 will cook, and that for all y_3, y_3 is not a politician we can infer that for all y_3, y_3 will cook. Therefore, the answer is yes.