Consider the following premises. For all z, if z takes a plane, then z is running. Richard is taking a plane or Richard is not running. Can we infer the following from them? If is not true that Richard is running if and only if Richard is taking a plane.
 From the fact that for all z, if z takes a plane, then z is running we can infer that if Richard takes a plane, then Richard is running. From the fact that Richard is taking a plane or Richard is not running we can infer that if Richard goes running, then Richard is taking a plane. Finally, from the fact that if Richard goes running, then Richard is taking a plane, and that if Richard takes a plane, then Richard is running we can infer that Richard is running if and only if Richard is taking a plane, which contradicts that If is not true that Richard is running if and only if Richard is taking a plane. Therefore, the answer is no.