Consider the following premises. If Jessica were sad, then it is raining. For all x, x is sad. Can we infer the following from them? It is not raining.
 From the fact that for all x, x is sad we can infer that Jessica is sad. Finally, from the fact that if Jessica were sad, then it is raining, and that Jessica is sad we can infer that it is raining, which contradicts that It is not raining. Therefore, the answer is no.