Consider the following premises. For all x_3, if x_3 were a carpenter, then x_3 is a bartender. For all x_3, if x_3 were a bartender, then x_3 is a carpenter. For all x_3, if x_3 were sad, then x_3 is a bartender. For all x_3, x_3 is not a carpenter. Can we infer the following from them? For all x_3, x_3 is not sad.
 From the fact that for all x_3, if x_3 were a bartender, then x_3 is a carpenter, and that for all x_3, if x_3 were a carpenter, then x_3 is a bartender we can infer that for all x_3, x_3 is a bartender if and only if x_3 is a carpenter. From the fact that for all x_3, x_3 is a bartender if and only if x_3 is a carpenter, and that for all x_3, x_3 is not a carpenter we can infer that for all x_3, x_3 is not a bartender. Finally, from the fact that for all x_3, if x_3 were sad, then x_3 is a bartender, and that for all x_3, x_3 is not a bartender we can infer that for all x_3, x_3 is not sad. Therefore, the answer is yes.