Consider the following premises. Thomas is not working or it is late. Thomas is working or Patricia is writing a letter. For all x_8, if x_8 writes a letter, then x_8 is excited. If it is late, then Patricia is excited. Can we infer the following from them? If we can, name the inference rule being used: Patricia is excited.
 From the fact that for all x_8, if x_8 writes a letter, then x_8 is excited we can infer that if Patricia writes a letter, then Patricia is excited via universal instantiation. From the fact that Thomas is working or Patricia is writing a letter, and that Thomas is not working or it is late we can infer that Patricia is writing a letter or it is late via resolution. Finally, from the fact that if Patricia writes a letter, then Patricia is excited, that if it is late, then Patricia is excited, and that Patricia is writing a letter or it is late we can infer that Patricia is excited via disjunction elimination. Therefore, the answer is yes.