Consider the following premises. It is sunny or Charles is not sleeping. Sarah is playing a game if and only if Charles is sleeping. If it is sunny, then Charles is sleeping. Linda is not poor. Linda is poor if and only if Sarah is playing a game. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that Linda is poor if and only if Sarah is playing a game, and that Linda is not poor we can infer that Sarah is not playing a game via biconditional elimination. From the fact that Sarah is playing a game if and only if Charles is sleeping, and that Sarah is not playing a game we can infer that Charles is not sleeping via biconditional elimination. From the fact that it is sunny or Charles is not sleeping we can infer that if Charles sleeps, then it is sunny via rewriting. From the fact that if Charles sleeps, then it is sunny, and that if it is sunny, then Charles is sleeping we can infer that Charles is sleeping if and only if it is sunny via biconditional introduction. Finally, from the fact that Charles is sleeping if and only if it is sunny, and that Charles is not sleeping we can infer that it is not sunny via biconditional elimination, which contradicts that It is sunny. Therefore, the answer is no.