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