Consider the following premises. For all x_7, x_7 will work or x_7 is a politician. For all x_7, if x_7 were a politician, then x_7 is a carpenter. For all x_7, x_7 will not work or x_7 is sad. There is at least one x_7 for which x_7 is a carpenter or x_7 is not sad. Can we infer the following from them? There is at least one x_7 for which x_7 is a carpenter.
 From the fact that for all x_7, x_7 will work or x_7 is a politician, and that for all x_7, x_7 will not work or x_7 is sad we can infer that for all x_7, x_7 is a politician or x_7 is sad. From the fact that there is at least one x_7 for which x_7 is a carpenter or x_7 is not sad we can infer that there is at least one x_7 for which if x_7 were sad, then x_7 is a carpenter. Finally, from the fact that for all x_7, if x_7 were a politician, then x_7 is a carpenter, that there is at least one x_7 for which if x_7 were sad, then x_7 is a carpenter, and that for all x_7, x_7 is a politician or x_7 is sad we can infer that there is at least one x_7 for which x_7 is a carpenter. Therefore, the answer is yes.