Consider the following premises. For all x_2, x_2 is sad if and only if x_2 will drive a car. There is at least one x_2 for which x_2 will drive a car or x_2 is not sad. Can we infer the following from them? There is at least one x_2 for which x_2 will drive a car if and only if x_2 is sad.
 From the fact that there is at least one x_2 for which x_2 will drive a car or x_2 is not sad we can infer that there is at least one x_2 for which if x_2 were sad, then x_2 is driving a car. From the fact that for all x_2, x_2 is sad if and only if x_2 will drive a car we can infer that for all x_2, if x_2 drives a car, then x_2 is sad. Finally, from the fact that for all x_2, if x_2 drives a car, then x_2 is sad, and that there is at least one x_2 for which if x_2 were sad, then x_2 is driving a car we can infer that there is at least one x_2 for which x_2 will drive a car if and only if x_2 is sad. Therefore, the answer is yes.