Consider the following premises. David is sad or John is not a nurse. John is a nurse or David is a lawyer. If David were a lawyer, then David is sad. Can we infer the following from them? David is not sad.
 From the fact that David is sad or John is not a nurse we can infer that if John were a nurse, then David is sad. Finally, from the fact that if John were a nurse, then David is sad, that if David were a lawyer, then David is sad, and that John is a nurse or David is a lawyer we can infer that David is sad, which contradicts that David is not sad. Therefore, the answer is no.