Consider the following premises. For all x_8, x_8 will take a plane if and only if x_8 will listen to a song. For all x_8, x_8 will listen to a song if and only if x_8 is a writer. For all x_8, x_8 is a writer if and only if x_8 is poor. For all x_8, x_8 is not poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will take a plane.
 From the fact that for all x_8, x_8 is a writer if and only if x_8 is poor, and that for all x_8, x_8 is not poor we can infer that for all x_8, x_8 is not a writer via universal biconditional elimination. From the fact that for all x_8, x_8 will listen to a song if and only if x_8 is a writer, and that for all x_8, x_8 is not a writer we can infer that for all x_8, x_8 will not listen to a song via universal biconditional elimination. Finally, from the fact that for all x_8, x_8 will take a plane if and only if x_8 will listen to a song, and that for all x_8, x_8 will not listen to a song we can infer that for all x_8, x_8 will not take a plane via universal biconditional elimination, which contradicts that There is at least one x_8 for which x_8 will take a plane. Therefore, the answer is no.