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 not windy. It is not cloudy. It is windy if and only if it is cold. Sarah is playing a game if and only if it is cloudy.
It is not windy and it is not cloudy can be inferred via the conjunction rule. It is not cloudy and it is not windy can be inferred via the conjunction rule. If it is windy, then it is cold can be inferred via the biconditional elimination rule. If Sarah plays a game, then it is cloudy can be inferred via the biconditional elimination rule. If it is cold, then it is windy can be inferred via the biconditional elimination rule. If it is cloudy, then Sarah is playing a game can be inferred via the biconditional elimination rule. It is not cold can be inferred via the biconditional elimination rule. Sarah is not playing a game can be inferred via the biconditional elimination rule.