Consider the following premises. If Patricia were a politician, then it is raining. Patricia is taking a plane or it is windy. For all x_10, if x_10 takes a plane, then x_10 is a politician. If it is windy, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that for all x_10, if x_10 takes a plane, then x_10 is a politician we can infer that if Patricia takes a plane, then Patricia is a politician via universal instantiation. From the fact that if Patricia takes a plane, then Patricia is a politician, and that if Patricia were a politician, then it is raining we can infer that if Patricia takes a plane, then it is raining via transitivity. Finally, from the fact that if Patricia takes a plane, then it is raining, that if it is windy, then it is raining, and that Patricia is taking a plane or it is windy we can infer that it is raining via disjunction elimination, which contradicts that It is not raining. Therefore, the answer is no.