Consider the following premises. There is at least one y_2 for which y_2 is not a writer. For all y_2, if y_2 were a writer, then y_2 is taking a plane. For all y_2, if y_2 takes a plane, then y_2 is drinking water. For all y_2, y_2 will drink water if and only if y_2 is a writer. Can we infer the following from them? For all y_2, y_2 will take a plane.
 From the fact that for all y_2, y_2 will drink water if and only if y_2 is a writer we can infer that for all y_2, if y_2 drinks water, then y_2 is a writer. From the fact that for all y_2, if y_2 takes a plane, then y_2 is drinking water, and that for all y_2, if y_2 drinks water, then y_2 is a writer we can infer that for all y_2, if y_2 takes a plane, then y_2 is a writer. From the fact that for all y_2, if y_2 were a writer, then y_2 is taking a plane, and that for all y_2, if y_2 takes a plane, then y_2 is a writer we can infer that for all y_2, y_2 is a writer if and only if y_2 will take a plane. Finally, from the fact that for all y_2, y_2 is a writer if and only if y_2 will take a plane, and that there is at least one y_2 for which y_2 is not a writer we can infer that there is at least one y_2 for which y_2 will not take a plane, which contradicts that For all y_2, y_2 will take a plane. Therefore, the answer is no.