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: Susan is a bartender if and only if Patricia is cooking. Susan is not a bartender. Elisabeth is running if and only if John is sad. John is not sad.
Susan is not a bartender and John is not sad can be inferred via the conjunction rule. John is not sad and Susan is not a bartender can be inferred via the conjunction rule. If Susan were a bartender, then Patricia is cooking can be inferred via the biconditional elimination rule. If Elisabeth goes running, then John is sad can be inferred via the biconditional elimination rule. If Patricia cooks, then Susan is a bartender can be inferred via the biconditional elimination rule. If John were sad, then Elisabeth is running can be inferred via the biconditional elimination rule. Patricia is not cooking can be inferred via the biconditional elimination rule. Elisabeth is not running can be inferred via the biconditional elimination rule.