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: If Mary listens to a song, then Karen is an electrician. Sarah is sad if and only if Richard is a poet. Sarah is not sad. Karen is not an electrician.
Mary is not listening to a song can be inferred via the modus tollens rule. Sarah is not sad and Karen is not an electrician can be inferred via the conjunction rule. Karen is not an electrician and Sarah is not sad can be inferred via the conjunction rule. If Sarah were sad, then Richard is a poet can be inferred via the biconditional elimination rule. If Richard were a poet, then Sarah is sad can be inferred via the biconditional elimination rule. Richard is not a poet can be inferred via the biconditional elimination rule.