Consider the following premises. Patricia is not writing a letter. Patricia is sad or Patricia is not writing a letter. Patricia is writing a letter or Patricia is not sad. Can we infer the following from them? If we can, name the inference rule being used: Patricia is sad.
 From the fact that Patricia is writing a letter or Patricia is not sad we can infer that if Patricia were sad, then Patricia is writing a letter via rewriting. From the fact that Patricia is sad or Patricia is not writing a letter we can infer that if Patricia writes a letter, then Patricia is sad via rewriting. From the fact that if Patricia were sad, then Patricia is writing a letter, and that if Patricia writes a letter, then Patricia is sad we can infer that Patricia is sad if and only if Patricia is writing a letter via biconditional introduction. Finally, from the fact that Patricia is sad if and only if Patricia is writing a letter, and that Patricia is not writing a letter we can infer that Patricia is not sad via biconditional elimination, which contradicts that Patricia is sad. Therefore, the answer is no.