Consider the following premises. For all x_9, if x_9 cooks, then x_9 is not playing squash. Barbara is playing squash. For all x_9, x_9 will play a game if and only if x_9 will cook. Can we infer the following from them? For all x_9, x_9 will play a game.
 From the fact that Barbara is playing squash we can infer that there is at least one x_9 for which x_9 will play squash. From the fact that for all x_9, if x_9 cooks, then x_9 is not playing squash, and that there is at least one x_9 for which x_9 will play squash we can infer that there is at least one x_9 for which x_9 will not cook. Finally, from the fact that for all x_9, x_9 will play a game if and only if x_9 will cook, and that there is at least one x_9 for which x_9 will not cook we can infer that there is at least one x_9 for which x_9 will not play a game, which contradicts that For all x_9, x_9 will play a game. Therefore, the answer is no.