Consider the following premises. Mary is cooking if and only if it is cold. It is cold if and only if Mary is cooking. Mary is cooking or Charles is playing a game. It is not cold. Can we infer the following from them? Charles is not playing a game.
 From the fact that Mary is cooking if and only if it is cold we can infer that if Mary cooks, then it is cold. From the fact that it is cold if and only if Mary is cooking we can infer that if it is cold, then Mary is cooking. From the fact that if Mary cooks, then it is cold, and that if it is cold, then Mary is cooking we can infer that Mary is cooking if and only if it is cold. From the fact that Mary is cooking if and only if it is cold, and that it is not cold we can infer that Mary is not cooking. Finally, from the fact that Mary is cooking or Charles is playing a game, and that Mary is not cooking we can infer that Charles is playing a game, which contradicts that Charles is not playing a game. Therefore, the answer is no.