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: Barbara is a soldier. Karen is a carpenter if and only if Michael is listening to a song. If Michael listens to a song, then Barbara is not a soldier. It is cold.
Michael is not listening to a song can be inferred via the modus tollens rule. Barbara is a soldier and it is cold can be inferred via the conjunction rule. It is cold and Barbara is a soldier can be inferred via the conjunction rule. If Karen were a carpenter, then Michael is listening to a song can be inferred via the biconditional elimination rule. If Michael listens to a song, then Karen is a carpenter can be inferred via the biconditional elimination rule.