Consider the following premises. For all x_11, x_11 will take a plane if and only if x_11 is poor. Sarah is not taking a plane. If Sarah were not poor, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that for all x_11, x_11 will take a plane if and only if x_11 is poor we can infer that Sarah is taking a plane if and only if Sarah is poor via universal instantiation. From the fact that Sarah is taking a plane if and only if Sarah is poor, and that Sarah is not taking a plane we can infer that Sarah is not poor via biconditional elimination. Finally, from the fact that if Sarah were not poor, then it is cold, and that Sarah is not poor we can infer that it is cold via modus ponens, which contradicts that It is not cold. Therefore, the answer is no.