Consider the following premises. Sarah is curious or Jessica is not playing a game. If it rains, then Jessica is playing a game. Sarah is curious if and only if it is raining. Sarah is not curious. Can we infer the following from them? If we can, name the inference rule being used: Jessica is playing a game.
 From the fact that Sarah is curious if and only if it is raining we can infer that if Sarah were curious, then it is raining via biconditional elimination. From the fact that if Sarah were curious, then it is raining, and that if it rains, then Jessica is playing a game we can infer that if Sarah were curious, then Jessica is playing a game via transitivity. From the fact that Sarah is curious or Jessica is not playing a game we can infer that if Jessica plays a game, then Sarah is curious via rewriting. From the fact that if Jessica plays a game, then Sarah is curious, and that if Sarah were curious, then Jessica is playing a game we can infer that Jessica is playing a game if and only if Sarah is curious via biconditional introduction. Finally, from the fact that Jessica is playing a game if and only if Sarah is curious, and that Sarah is not curious we can infer that Jessica is not playing a game via biconditional elimination, which contradicts that Jessica is playing a game. Therefore, the answer is no.