Consider the following premises. Barbara is cooking. For all y, y is sad or y will not cook. Can we infer the following from them? There is at least one y for which y is sad.
 From the fact that Barbara is cooking we can infer that there is at least one y for which y will cook. From the fact that for all y, y is sad or y will not cook we can infer that for all y, if y cooks, then y is sad. Finally, from the fact that for all y, if y cooks, then y is sad, and that there is at least one y for which y will cook we can infer that there is at least one y for which y is sad. Therefore, the answer is yes.