Consider the following premises. If Mary reads a book, then Charles is a doctor. If Charles were a doctor, then Mary is reading a book. Charles is a doctor if and only if Mary is playing a game. Can we infer the following from them? The fact that Mary reads a book does not imply that Mary is playing a game.
 From the fact that if Charles were a doctor, then Mary is reading a book, and that if Mary reads a book, then Charles is a doctor we can infer that Charles is a doctor if and only if Mary is reading a book. From the fact that Charles is a doctor if and only if Mary is reading a book we can infer that if Mary reads a book, then Charles is a doctor. From the fact that Charles is a doctor if and only if Mary is playing a game we can infer that if Charles were a doctor, then Mary is playing a game. Finally, from the fact that if Mary reads a book, then Charles is a doctor, and that if Charles were a doctor, then Mary is playing a game we can infer that if Mary reads a book, then Mary is playing a game, which contradicts that The fact that Mary reads a book does not imply that Mary is playing a game. Therefore, the answer is no.