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: William is excited if and only if Patricia is listening to a song. Patricia is not listening to a song. If William were excited, then Elisabeth is working. If Elisabeth works, then William is excited.
William is excited if and only if Elisabeth is working can be inferred via the biconditional introduction rule. Elisabeth is working if and only if William is excited can be inferred via the biconditional introduction rule. If William were excited, then Patricia is listening to a song can be inferred via the biconditional elimination rule. If Patricia listens to a song, then William is excited can be inferred via the biconditional elimination rule. William is not excited can be inferred via the biconditional elimination rule.