Consider the following premises. For all y_1, if y_1 cooks, then y_1 is a sailor. For all y_1, y_1 is not a politician. There is at least one y_1 for which y_1 will cook if and only if y_1 is a politician. For all y_1, if y_1 were a sailor, then y_1 is cooking. Can we infer the following from them? For all y_1, y_1 is a sailor.
 From the fact that for all y_1, if y_1 cooks, then y_1 is a sailor, and that for all y_1, if y_1 were a sailor, then y_1 is cooking we can infer that for all y_1, y_1 will cook if and only if y_1 is a sailor. From the fact that there is at least one y_1 for which y_1 will cook if and only if y_1 is a politician, and that for all y_1, y_1 is not a politician we can infer that there is at least one y_1 for which y_1 will not cook. Finally, from the fact that for all y_1, y_1 will cook if and only if y_1 is a sailor, and that there is at least one y_1 for which y_1 will not cook we can infer that there is at least one y_1 for which y_1 is not a sailor, which contradicts that For all y_1, y_1 is a sailor. Therefore, the answer is no.