Consider the following premises. For all x_4, if x_4 were bored, then x_4 is poor. For all x_4, x_4 is bored if and only if x_4 is sad. Can we infer the following from them? There is at least one x_4 for which the fact that x_4 were sad does not imply that x_4 is poor.
 From the fact that for all x_4, x_4 is bored if and only if x_4 is sad we can infer that for all x_4, if x_4 were sad, then x_4 is bored. Finally, from the fact that for all x_4, if x_4 were sad, then x_4 is bored, and that for all x_4, if x_4 were bored, then x_4 is poor we can infer that for all x_4, if x_4 were sad, then x_4 is poor, which contradicts that There is at least one x_4 for which the fact that x_4 were sad does not imply that x_4 is poor. Therefore, the answer is no.