Consider the following premises. If Jennifer were a scientist, then David is sad. If Robert plays a game, then David is sad. Jennifer is a scientist or Robert is playing a game. If David were sad, then Jennifer is a scientist. Can we infer the following from them? If we can, name the inference rule being used: David is not sad.
 From the fact that if Jennifer were a scientist, then David is sad, and that if David were sad, then Jennifer is a scientist we can infer that Jennifer is a scientist if and only if David is sad via biconditional introduction. From the fact that Jennifer is a scientist if and only if David is sad we can infer that if Jennifer were a scientist, then David is sad via biconditional elimination. Finally, from the fact that if Jennifer were a scientist, then David is sad, that if Robert plays a game, then David is sad, and that Jennifer is a scientist or Robert is playing a game we can infer that David is sad via disjunction elimination, which contradicts that David is not sad. Therefore, the answer is no.