Consider the following premises. For all x_1, x_1 will read a book. For all x_1, x_1 will play a game. Can we infer the following from them? There is at least one x_1 for which x_1 will not play a game.
 From the fact that for all x_1, x_1 will play a game, and that for all x_1, x_1 will read a book we can infer that for all x_1, x_1 will play a game and x_1 will read a book. Finally, from the fact that for all x_1, x_1 will play a game and x_1 will read a book we can infer that for all x_1, x_1 will play a game, which contradicts that There is at least one x_1 for which x_1 will not play a game. Therefore, the answer is no.