Consider the following premises. Patricia is not reading a book. Susan is drinking water if and only if William is driving a car. It is late if and only if Patricia is reading a book. William is not driving a car. Can we infer the following from them? It is not late or Joseph is playing a game.
 From the fact that it is late if and only if Patricia is reading a book, and that Patricia is not reading a book we can infer that it is not late. From the fact that Susan is drinking water if and only if William is driving a car, and that William is not driving a car we can infer that Susan is not drinking water. From the fact that it is not late, and that Susan is not drinking water we can infer that it is not late and Susan is not drinking water. From the fact that it is not late and Susan is not drinking water we can infer that it is not late. Finally, from the fact that it is not late we can infer that it is not late or Joseph is playing a game. Therefore, the answer is yes.