Consider the following premises. Sarah is happy. If Jennifer writes a letter, then Sarah is not happy. It is cold. Joseph is working if and only if it is cold. If Mary were poor, then Joseph is working. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not working.
 From the fact that it is cold we can infer that it is cold or Mary is poor via addition. From the fact that if Jennifer writes a letter, then Sarah is not happy, and that Sarah is happy we can infer that Jennifer is not writing a letter via modus tollens. From the fact that Joseph is working if and only if it is cold we can infer that if it is cold, then Joseph is working via biconditional elimination. Finally, from the fact that if it is cold, then Joseph is working, that if Mary were poor, then Joseph is working, and that it is cold or Mary is poor we can infer that Joseph is working via disjunction elimination, which contradicts that Joseph is not working. Therefore, the answer is no.