Consider the following premises. For all x_10, if x_10 takes a plane, then x_10 is driving a car. For all x_10, x_10 will not drive a car. It is cloudy if and only if Charles is taking a plane. For all x_10, if x_10 drives a car, then x_10 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy.
 From the fact that for all x_10, if x_10 takes a plane, then x_10 is driving a car, and that for all x_10, if x_10 drives a car, then x_10 is taking a plane we can infer that for all x_10, x_10 will take a plane if and only if x_10 will drive a car via universal biconditional introduction. From the fact that for all x_10, x_10 will take a plane if and only if x_10 will drive a car, and that for all x_10, x_10 will not drive a car we can infer that for all x_10, x_10 will not take a plane via universal biconditional elimination. From the fact that for all x_10, x_10 will not take a plane we can infer that Charles is not taking a plane via universal instantiation. Finally, from the fact that it is cloudy if and only if Charles is taking a plane, and that Charles is not taking a plane we can infer that it is not cloudy via biconditional elimination, which contradicts that It is cloudy. Therefore, the answer is no.