Consider the following premises. For all x_10, if x_10 writes a letter, then x_10 is taking a plane. Elisabeth is not writing a letter. For all x_10, if x_10 takes a plane, then x_10 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not taking a plane.
 From the fact that for all x_10, if x_10 takes a plane, then x_10 is writing a letter, and that for all x_10, if x_10 writes a letter, 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 write a letter 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 write a letter we can infer that for all x_10, if x_10 takes a plane, then x_10 is writing a letter via universal biconditional elimination. From the fact that for all x_10, if x_10 takes a plane, then x_10 is writing a letter we can infer that if Elisabeth takes a plane, then Elisabeth is writing a letter via universal instantiation. Finally, from the fact that if Elisabeth takes a plane, then Elisabeth is writing a letter, and that Elisabeth is not writing a letter we can infer that Elisabeth is not taking a plane via modus tollens. Therefore, the answer is yes.