Consider the following premises. Michael is not an electrician. Mary is a bartender if and only if it is raining. If Mary were a bartender, then Michael is an electrician. If Michael were an electrician, then Mary is a bartender. Can we infer the following from them? It is not raining.
 From the fact that if Michael were an electrician, then Mary is a bartender, and that if Mary were a bartender, then Michael is an electrician we can infer that Michael is an electrician if and only if Mary is a bartender. From the fact that Michael is an electrician if and only if Mary is a bartender we can infer that if Mary were a bartender, then Michael is an electrician. From the fact that if Mary were a bartender, then Michael is an electrician, and that Michael is not an electrician we can infer that Mary is not a bartender. Finally, from the fact that Mary is a bartender if and only if it is raining, and that Mary is not a bartender we can infer that it is not raining. Therefore, the answer is yes.