Consider the following premises. For all x_8, x_8 will cook if and only if x_8 will play a game. For all x_8, x_8 will play a game if and only if x_8 will cook. Can we infer the following from them? There is at least one x_8 for which the fact that x_8 plays a game does not imply that x_8 is cooking.
 From the fact that for all x_8, x_8 will cook if and only if x_8 will play a game we can infer that for all x_8, if x_8 cooks, then x_8 is playing a game. From the fact that for all x_8, x_8 will play a game if and only if x_8 will cook we can infer that for all x_8, if x_8 plays a game, then x_8 is cooking. From the fact that for all x_8, if x_8 cooks, then x_8 is playing a game, and that for all x_8, if x_8 plays a game, then x_8 is cooking we can infer that for all x_8, x_8 will cook if and only if x_8 will play a game. Finally, from the fact that for all x_8, x_8 will cook if and only if x_8 will play a game we can infer that for all x_8, if x_8 plays a game, then x_8 is cooking, which contradicts that There is at least one x_8 for which the fact that x_8 plays a game does not imply that x_8 is cooking. Therefore, the answer is no.