Consider the following premises. For all x_12, x_12 will drive a car or x_12 will take a plane. For all x_12, x_12 will not drive a car. There is at least one x_12 for which if x_12 were happy, then x_12 is reading a book. For all x_12, x_12 is fast or x_12 is happy. For all x_12, if x_12 were fast, then x_12 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will take a plane and x_12 will read a book.
 From the fact that for all x_12, if x_12 were fast, then x_12 is reading a book, that there is at least one x_12 for which if x_12 were happy, then x_12 is reading a book, and that for all x_12, x_12 is fast or x_12 is happy we can infer that there is at least one x_12 for which x_12 will read a book via existential disjunction elimination. From the fact that for all x_12, x_12 will drive a car or x_12 will take a plane, and that for all x_12, x_12 will not drive a car we can infer that for all x_12, x_12 will take a plane via universal disjunctive syllogism. Finally, from the fact that for all x_12, x_12 will take a plane, and that there is at least one x_12 for which x_12 will read a book we can infer that there is at least one x_12 for which x_12 will take a plane and x_12 will read a book via existential conjunction. Therefore, the answer is yes.