Consider the following premises. For all y_1, y_1 will write a letter or y_1 will sleep. It is not windy. Susan is writing a letter if and only if it is late. If it is late, then it is windy. Can we infer the following from them? If we can, name the inference rule being used: Susan is sleeping.
 From the fact that for all y_1, y_1 will write a letter or y_1 will sleep we can infer that Susan is writing a letter or Susan is sleeping via universal instantiation. From the fact that if it is late, then it is windy, and that it is not windy we can infer that it is not late via modus tollens. From the fact that Susan is writing a letter if and only if it is late, and that it is not late we can infer that Susan is not writing a letter via biconditional elimination. Finally, from the fact that Susan is writing a letter or Susan is sleeping, and that Susan is not writing a letter we can infer that Susan is sleeping via disjunctive syllogism. Therefore, the answer is yes.