Consider the following premises. For all y_2, y_2 will work if and only if y_2 will take a plane. For all y_2, if y_2 works, then y_2 is not playing squash. For all y_2, y_2 will play squash. Can we infer the following from them? There is at least one y_2 for which y_2 will take a plane.
 From the fact that for all y_2, if y_2 works, then y_2 is not playing squash, and that for all y_2, y_2 will play squash we can infer that for all y_2, y_2 will not work. Finally, from the fact that for all y_2, y_2 will work if and only if y_2 will take a plane, and that for all y_2, y_2 will not work we can infer that for all y_2, y_2 will not take a plane, which contradicts that There is at least one y_2 for which y_2 will take a plane. Therefore, the answer is no.