Consider the following premises. It is sunny if and only if Patricia is a soldier. For all x_20, x_20 will drive a car or x_20 is not a soldier. For all x_20, x_20 will not drive a car. Can we infer the following from them? If we can, name the inference rule being used: It is not sunny or it is cloudy.
 From the fact that for all x_20, x_20 will drive a car or x_20 is not a soldier we can infer that for all x_20, if x_20 were a soldier, then x_20 is driving a car via universal rewriting. From the fact that for all x_20, if x_20 were a soldier, then x_20 is driving a car, and that for all x_20, x_20 will not drive a car we can infer that for all x_20, x_20 is not a soldier via universal modus tollens. From the fact that for all x_20, x_20 is not a soldier we can infer that Patricia is not a soldier via universal instantiation. From the fact that it is sunny if and only if Patricia is a soldier, and that Patricia is not a soldier we can infer that it is not sunny via biconditional elimination. Finally, from the fact that it is not sunny we can infer that it is not sunny or it is cloudy via addition. Therefore, the answer is yes.