Consider the following premises. It is not overcast. If Mary were a scientist, then William is reading a book. It is overcast if and only if William is reading a book. Robert is playing a game if and only if Mary is a scientist. Can we infer the following from them? Robert is playing a game.
 From the fact that it is overcast if and only if William is reading a book, and that it is not overcast we can infer that William is not reading a book. From the fact that if Mary were a scientist, then William is reading a book, and that William is not reading a book we can infer that Mary is not a scientist. Finally, from the fact that Robert is playing a game if and only if Mary is a scientist, and that Mary is not a scientist we can infer that Robert is not playing a game, which contradicts that Robert is playing a game. Therefore, the answer is no.