Consider the following premises. John is cooking if and only if it is late. If Karen were happy, then John is cooking. For all x_7, x_7 will play a game if and only if x_7 is happy. It is not late. Can we infer the following from them? Karen is playing a game.
 From the fact that John is cooking if and only if it is late, and that it is not late we can infer that John is not cooking. From the fact that for all x_7, x_7 will play a game if and only if x_7 is happy we can infer that Karen is playing a game if and only if Karen is happy. From the fact that if Karen were happy, then John is cooking, and that John is not cooking we can infer that Karen is not happy. Finally, from the fact that Karen is playing a game if and only if Karen is happy, and that Karen is not happy we can infer that Karen is not playing a game, which contradicts that Karen is playing a game. Therefore, the answer is no.