Translate the following inference to logic notation: For all x, x_5 is curious. There is at least one x for which x_5 is fast. For all x, if x_5 were curious, then x_5 is a janitor. For all x, if x_5 reads a book, then x_5 is a janitor. Therefore there is at least one x for which x_5 is fast and x_5 is a janitor.
forall x: P(x). exists x: Q(x). forall x: P(x) -> R(x). forall x: S(x) -> R(x). Therefore exists x: Q(x) and R(x).