Consider the following premises. There is at least one x_1 for which x_1 is not excited. For all x_1, x_1 will write a letter if and only if x_1 is excited. For all x_1, x_1 will write a letter or x_1 will not drive a car. Can we infer the following from them? For all x_1, x_1 will drive a car.
 From the fact that for all x_1, x_1 will write a letter or x_1 will not drive a car we can infer that for all x_1, if x_1 drives a car, then x_1 is writing a letter. From the fact that for all x_1, x_1 will write a letter if and only if x_1 is excited, and that there is at least one x_1 for which x_1 is not excited we can infer that there is at least one x_1 for which x_1 will not write a letter. Finally, from the fact that for all x_1, if x_1 drives a car, then x_1 is writing a letter, and that there is at least one x_1 for which x_1 will not write a letter we can infer that there is at least one x_1 for which x_1 will not drive a car, which contradicts that For all x_1, x_1 will drive a car. Therefore, the answer is no.