Consider the following premises. If Mary goes running, then it is overcast. Mary is running. William is not a doctor. Mary is taking a plane if and only if William is a doctor. Can we infer the following from them? It is not overcast.
 From the fact that Mary is taking a plane if and only if William is a doctor, and that William is not a doctor we can infer that Mary is not taking a plane. Finally, from the fact that if Mary goes running, then it is overcast, and that Mary is running we can infer that it is overcast, which contradicts that It is not overcast. Therefore, the answer is no.