Consider the following premises. For all y, if y takes a plane, then y is running. There is at least one y for which y will take a plane or y will not go running. For all y, y will take a plane or y will not go running. Can we infer the following from them? For all y, if is not true that y will take a plane if and only if y will go running.
 From the fact that there is at least one y for which y will take a plane or y will not go running we can infer that there is at least one y for which if y goes running, then y is taking a plane. From the fact that for all y, y will take a plane or y will not go running we can infer that for all y, if y goes running, then y is taking a plane. Finally, from the fact that for all y, if y takes a plane, then y is running, and that for all y, if y goes running, then y is taking a plane we can infer that for all y, y will take a plane if and only if y will go running, which contradicts that For all y, if is not true that y will take a plane if and only if y will go running. Therefore, the answer is no.