Consider the following premises. For all y_3, y_3 is not a mechanic. If Patricia drinks water, then Susan is cooking. If Susan cooks, then it is raining. If it is cold, then Patricia is drinking water. Barbara is a mechanic if and only if it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that for all y_3, y_3 is not a mechanic we can infer that Barbara is not a mechanic via universal instantiation. From the fact that Barbara is a mechanic if and only if it is raining, and that Barbara is not a mechanic we can infer that it is not raining via biconditional elimination. From the fact that if it is cold, then Patricia is drinking water, and that if Patricia drinks water, then Susan is cooking we can infer that if it is cold, then Susan is cooking via transitivity. From the fact that if Susan cooks, then it is raining, and that it is not raining we can infer that Susan is not cooking via modus tollens. Finally, from the fact that if it is cold, then Susan is cooking, and that Susan is not cooking we can infer that it is not cold via modus tollens, which contradicts that It is cold. Therefore, the answer is no.