Consider the following premises. For all z, z will not listen to a song. For all z, z will take a plane if and only if z will listen to a song. For all z, z will listen to a song if and only if z will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all z, z will not take a plane.
 From the fact that for all z, z will listen to a song if and only if z will take a plane we can infer that for all z, if z takes a plane, then z is listening to a song via universal biconditional elimination. From the fact that for all z, z will take a plane if and only if z will listen to a song we can infer that for all z, if z listens to a song, then z is taking a plane via universal biconditional elimination. From the fact that for all z, if z listens to a song, then z is taking a plane, and that for all z, if z takes a plane, then z is listening to a song we can infer that for all z, z will listen to a song if and only if z will take a plane via universal biconditional introduction. Finally, from the fact that for all z, z will listen to a song if and only if z will take a plane, and that for all z, z will not listen to a song we can infer that for all z, z will not take a plane via universal biconditional elimination. Therefore, the answer is yes.