Consider the following premises. For all x_7, if x_7 takes a plane, then x_7 is not writing a letter. For all x_7, x_7 will write a letter and x_7 will listen to a song. There is at least one x_7 for which x_7 will take a plane if and only if x_7 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is a musician.
 From the fact that for all x_7, x_7 will write a letter and x_7 will listen to a song we can infer that for all x_7, x_7 will write a letter via universal simplification. From the fact that for all x_7, if x_7 takes a plane, then x_7 is not writing a letter, and that for all x_7, x_7 will write a letter we can infer that for all x_7, x_7 will not take a plane via universal modus tollens. Finally, from the fact that there is at least one x_7 for which x_7 will take a plane if and only if x_7 is a musician, and that for all x_7, x_7 will not take a plane we can infer that there is at least one x_7 for which x_7 is not a musician via existential biconditional elimination, which contradicts that For all x_7, x_7 is a musician. Therefore, the answer is no.