Consider the following premises. For all x_8, x_8 will not cook. For all x_8, x_8 will cook if and only if x_8 is sad. For all x_8, if x_8 were poor, then x_8 is sad. For all x_8, x_8 is sad if and only if x_8 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is poor.
 From the fact that for all x_8, x_8 is sad if and only if x_8 is poor we can infer that for all x_8, if x_8 were sad, then x_8 is poor via universal biconditional elimination. From the fact that for all x_8, x_8 will cook if and only if x_8 is sad, and that for all x_8, x_8 will not cook we can infer that for all x_8, x_8 is not sad via universal biconditional elimination. From the fact that for all x_8, if x_8 were poor, then x_8 is sad, and that for all x_8, if x_8 were sad, then x_8 is poor we can infer that for all x_8, x_8 is poor if and only if x_8 is sad via universal biconditional introduction. Finally, from the fact that for all x_8, x_8 is poor if and only if x_8 is sad, and that for all x_8, x_8 is not sad we can infer that for all x_8, x_8 is not poor via universal biconditional elimination, which contradicts that There is at least one x_8 for which x_8 is poor. Therefore, the answer is no.