Consider the following premises. For all y, if y writes a letter, then y is climbing a mountain. For all y, if y cooks, then y is excited. There is at least one y for which if y were excited, then y is cooking. For all y, y will not climb a mountain. For all y, y will cook if and only if y will write a letter. Can we infer the following from them? For all y, y is excited.
 From the fact that for all y, if y writes a letter, then y is climbing a mountain, and that for all y, y will not climb a mountain we can infer that for all y, y will not write a letter. From the fact that for all y, if y cooks, then y is excited, and that there is at least one y for which if y were excited, then y is cooking we can infer that there is at least one y for which y will cook if and only if y is excited. From the fact that for all y, y will cook if and only if y will write a letter, and that for all y, y will not write a letter we can infer that for all y, y will not cook. Finally, from the fact that there is at least one y for which y will cook if and only if y is excited, and that for all y, y will not cook we can infer that there is at least one y for which y is not excited, which contradicts that For all y, y is excited. Therefore, the answer is no.