Consider the following premises. For all x_10, x_10 will write a letter or x_10 is a police officer. If Sarah were poor, then it is windy. For all x_10, x_10 will not write a letter or x_10 is poor. Sarah is a police officer if and only if it is windy. Can we infer the following from them? If we can, name the inference rule being used: It is not windy.
 From the fact that for all x_10, x_10 will write a letter or x_10 is a police officer, and that for all x_10, x_10 will not write a letter or x_10 is poor we can infer that for all x_10, x_10 is a police officer or x_10 is poor via universal resolution. From the fact that for all x_10, x_10 is a police officer or x_10 is poor we can infer that Sarah is a police officer or Sarah is poor via universal instantiation. From the fact that Sarah is a police officer if and only if it is windy we can infer that if Sarah were a police officer, then it is windy via biconditional elimination. Finally, from the fact that if Sarah were a police officer, then it is windy, that if Sarah were poor, then it is windy, and that Sarah is a police officer or Sarah is poor we can infer that it is windy via disjunction elimination, which contradicts that It is not windy. Therefore, the answer is no.