Consider the following premises. If it is windy, then it is cold. If it is cold, then it is windy. It is windy if and only if Barbara is cooking. Can we infer the following from them? If Barbara cooks, then it is cold.
 From the fact that it is windy if and only if Barbara is cooking we can infer that if Barbara cooks, then it is windy. From the fact that if it is windy, then it is cold, and that if it is cold, then it is windy we can infer that it is windy if and only if it is cold. From the fact that it is windy if and only if it is cold we can infer that if it is windy, then it is cold. Finally, from the fact that if Barbara cooks, then it is windy, and that if it is windy, then it is cold we can infer that if Barbara cooks, then it is cold. Therefore, the answer is yes.