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: Joseph is sleeping if and only if Sarah is taking a plane. If Sarah doesn't take a plane, then it is late. Joseph is not writing a letter. Joseph is sleeping if and only if Joseph is writing a letter.
If Joseph sleeps, then Sarah is taking a plane can be inferred via the biconditional elimination rule. If Joseph sleeps, then Joseph is writing a letter can be inferred via the biconditional elimination rule. If Sarah takes a plane, then Joseph is sleeping can be inferred via the biconditional elimination rule. If Joseph writes a letter, then Joseph is sleeping can be inferred via the biconditional elimination rule. Joseph is not sleeping can be inferred via the biconditional elimination rule.