Consider the following premises. If it is sunny, then William is listening to a song. It is overcast if and only if it is sunny. If William listens to a song, then John is not reading a book. John is reading a book. Can we infer the following from them? It is overcast.
 From the fact that if William listens to a song, then John is not reading a book, and that John is reading a book we can infer that William is not listening to a song. From the fact that if it is sunny, then William is listening to a song, and that William is not listening to a song we can infer that it is not sunny. Finally, from the fact that it is overcast if and only if it is sunny, and that it is not sunny we can infer that it is not overcast, which contradicts that It is overcast. Therefore, the answer is no.