Consider the following premises. For all x, x will play a game if and only if x will cook. For all x, if x plays a game, then x is cooking. For all x, x will not cook. Can we infer the following from them? For all x, x will not play a game.
 From the fact that for all x, x will play a game if and only if x will cook we can infer that for all x, if x cooks, then x is playing a game. From the fact that for all x, if x cooks, then x is playing a game, and that for all x, if x plays a game, then x is cooking we can infer that for all x, x will cook if and only if x will play a game. Finally, from the fact that for all x, x will cook if and only if x will play a game, and that for all x, x will not cook we can infer that for all x, x will not play a game. Therefore, the answer is yes.