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