Translate the following inference to logic notation: For all x, x_6 will read a book. For all x, if x_6 reads a book, then x_6 is excited. There is at least one x for which x_6 is an astronaut if and only if x_6 is excited. Therefore there is at least one x for which x_6 is an astronaut.
forall x: P(x). forall x: P(x) -> Q(x). exists x: R(x) <-> Q(x). Therefore exists x: R(x).