Consider the following premises. If it rains, then it is cold. David is not playing squash. David is playing squash or it is not cold. Can we infer the following from them? It is raining.
 From the fact that David is playing squash or it is not cold we can infer that if it is cold, then David is playing squash. From the fact that if it rains, then it is cold, and that if it is cold, then David is playing squash we can infer that if it rains, then David is playing squash. Finally, from the fact that if it rains, then David is playing squash, and that David is not playing squash we can infer that it is not raining, which contradicts that It is raining. Therefore, the answer is no.