What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all z, z will not listen to a song. For all z, if z writes a letter, then z is listening to a song. For all z, if z listens to a song, then z is writing a letter.
For all z, z will not write a letter can be inferred via the universal modus tollens rule. For all z, z will write a letter if and only if z will listen to a song can be inferred via the universal biconditional introduction rule. For all z, z will listen to a song if and only if z will write a letter can be inferred via the universal biconditional introduction rule.