Translate the following inference to logic notation: For all x, if x_8 reads a book, then x_8 is writing a letter. For all x, if x_8 writes a letter, then x_8 is an astronaut. There is at least one x for which x_8 will read a book or x_8 is not an astronaut. Therefore there is at least one x for which if x_8 reads a book, then x_8 is an astronaut.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: P(x) or ~R(x). Therefore exists x: P(x) -> R(x).