Consider the following premises. It is overcast or Michael is a sailor. It is overcast if and only if William is running. Michael is a sailor if and only if William is running. Can we infer the following from them? William is running or it is cold.
 From the fact that it is overcast if and only if William is running we can infer that if it is overcast, then William is running. From the fact that Michael is a sailor if and only if William is running we can infer that if Michael were a sailor, then William is running. From the fact that if it is overcast, then William is running, that if Michael were a sailor, then William is running, and that it is overcast or Michael is a sailor we can infer that William is running. Finally, from the fact that William is running we can infer that William is running or it is cold. Therefore, the answer is yes.