Consider the following premises. If it is sunny, then Linda is not reading a book. If it is sunny, then Joseph is playing a game. Linda is reading a book. If Joseph plays a game, then it is sunny. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not playing a game.
 From the fact that if it is sunny, then Linda is not reading a book, and that Linda is reading a book we can infer that it is not sunny via modus tollens. From the fact that if Joseph plays a game, then it is sunny, and that if it is sunny, then Joseph is playing a game we can infer that Joseph is playing a game if and only if it is sunny via biconditional introduction. Finally, from the fact that Joseph is playing a game if and only if it is sunny, and that it is not sunny we can infer that Joseph is not playing a game via biconditional elimination. Therefore, the answer is yes.