Consider the following premises. If Mary were happy, then Barbara is running. If Barbara goes running, then it is cold. If it is cold, then it is overcast. If it is overcast, then Mary is happy. Can we infer the following from them? Barbara is running if and only if it is overcast.
 From the fact that if Barbara goes running, then it is cold, and that if it is cold, then it is overcast we can infer that if Barbara goes running, then it is overcast. From the fact that if it is overcast, then Mary is happy, and that if Mary were happy, then Barbara is running we can infer that if it is overcast, then Barbara is running. Finally, from the fact that if Barbara goes running, then it is overcast, and that if it is overcast, then Barbara is running we can infer that Barbara is running if and only if it is overcast. Therefore, the answer is yes.