Consider the following premises. If Michael cooks, then Michael is an office clerk. It is windy. Michael is not an office clerk. If it is late, then Michael is cooking. Can we infer the following from them? It is not late.
 From the fact that if it is late, then Michael is cooking, and that if Michael cooks, then Michael is an office clerk we can infer that if it is late, then Michael is an office clerk. Finally, from the fact that if it is late, then Michael is an office clerk, and that Michael is not an office clerk we can infer that it is not late. Therefore, the answer is yes.