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: It is cold if and only if Patricia is an electrician. If James listens to a song, then Joseph is excited. James is listening to a song. It is not cold.
Joseph is excited can be inferred via the modus ponens rule. James is listening to a song and it is not cold can be inferred via the conjunction rule. It is not cold and James is listening to a song can be inferred via the conjunction rule. If it is cold, then Patricia is an electrician can be inferred via the biconditional elimination rule. If Patricia were an electrician, then it is cold can be inferred via the biconditional elimination rule. Patricia is not an electrician can be inferred via the biconditional elimination rule.