Consider the following premises. There is at least one y_1 for which y_1 is poor if and only if y_1 will cook. For all y_1, if y_1 were poor, then y_1 is cooking. For all y_1, y_1 is not poor. Can we infer the following from them? If we can, name the inference rule being used: For all y_1, y_1 will cook.
 From the fact that there is at least one y_1 for which y_1 is poor if and only if y_1 will cook we can infer that there is at least one y_1 for which if y_1 cooks, then y_1 is poor via existential biconditional elimination. From the fact that for all y_1, if y_1 were poor, then y_1 is cooking, and that there is at least one y_1 for which if y_1 cooks, then y_1 is poor we can infer that there is at least one y_1 for which y_1 is poor if and only if y_1 will cook via existential biconditional introduction. Finally, from the fact that there is at least one y_1 for which y_1 is poor if and only if y_1 will cook, and that for all y_1, y_1 is not poor we can infer that there is at least one y_1 for which y_1 will not cook via existential biconditional elimination, which contradicts that For all y_1, y_1 will cook. Therefore, the answer is no.