Consider the following premises. Sarah is cooking if and only if Patricia is running. Patricia is running if and only if it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: If Sarah cooks, then it is cloudy.
 From the fact that Patricia is running if and only if it is cloudy we can infer that if Patricia goes running, then it is cloudy via biconditional elimination. From the fact that Sarah is cooking if and only if Patricia is running we can infer that if Sarah cooks, then Patricia is running via biconditional elimination. Finally, from the fact that if Sarah cooks, then Patricia is running, and that if Patricia goes running, then it is cloudy we can infer that if Sarah cooks, then it is cloudy via transitivity. Therefore, the answer is yes.