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: Karen is playing a game if and only if it is raining. Karen is not playing a game. It is cloudy.
Karen is not playing a game and it is cloudy can be inferred via the conjunction rule. It is cloudy and Karen is not playing a game can be inferred via the conjunction rule. If Karen plays a game, then it is raining can be inferred via the biconditional elimination rule. If it rains, then Karen is playing a game can be inferred via the biconditional elimination rule. It is not raining can be inferred via the biconditional elimination rule.