Consider the following premises. If Elisabeth listens to a song, then Jennifer is a server. If Jennifer were a server, then Elisabeth is a writer. For all x_10, if x_10 were a writer, then x_10 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Elisabeth is listening to a song if and only if Jennifer is a server.
 From the fact that for all x_10, if x_10 were a writer, then x_10 is listening to a song we can infer that if Elisabeth were a writer, then Elisabeth is listening to a song via universal instantiation. From the fact that if Jennifer were a server, then Elisabeth is a writer, and that if Elisabeth were a writer, then Elisabeth is listening to a song we can infer that if Jennifer were a server, then Elisabeth is listening to a song via transitivity. Finally, from the fact that if Elisabeth listens to a song, then Jennifer is a server, and that if Jennifer were a server, then Elisabeth is listening to a song we can infer that Elisabeth is listening to a song if and only if Jennifer is a server via biconditional introduction, which contradicts that If is not true that Elisabeth is listening to a song if and only if Jennifer is a server. Therefore, the answer is no.