Consider the following premises. For all z_4, z_4 will take a plane if and only if z_4 is poor. If Barbara were poor, then Barbara is taking a plane. Barbara is not poor. Can we infer the following from them? If we can, name the inference rule being used: Barbara is taking a plane.
 From the fact that for all z_4, z_4 will take a plane if and only if z_4 is poor we can infer that for all z_4, if z_4 takes a plane, then z_4 is poor via universal biconditional elimination. From the fact that for all z_4, if z_4 takes a plane, then z_4 is poor we can infer that if Barbara takes a plane, then Barbara is poor via universal instantiation. From the fact that if Barbara takes a plane, then Barbara is poor, and that if Barbara were poor, then Barbara is taking a plane we can infer that Barbara is taking a plane if and only if Barbara is poor via biconditional introduction. Finally, from the fact that Barbara is taking a plane if and only if Barbara is poor, and that Barbara is not poor we can infer that Barbara is not taking a plane via biconditional elimination, which contradicts that Barbara is taking a plane. Therefore, the answer is no.