Consider the following premises. Thomas is a scientist if and only if Karen is a mechanic. Karen is a mechanic if and only if Barbara is sleeping. It is not cold. Thomas is a scientist if and only if it is cold. Can we infer the following from them? Barbara is sleeping.
 From the fact that Thomas is a scientist if and only if it is cold, and that it is not cold we can infer that Thomas is not a scientist. From the fact that Thomas is a scientist if and only if Karen is a mechanic, and that Thomas is not a scientist we can infer that Karen is not a mechanic. Finally, from the fact that Karen is a mechanic if and only if Barbara is sleeping, and that Karen is not a mechanic we can infer that Barbara is not sleeping, which contradicts that Barbara is sleeping. Therefore, the answer is no.