Translate the following inference to logic notation: For all x, if y goes running, then y is a janitor. There is at least one x for which y is an astronaut. For all x, y is a mechanic. For all x, if y were an astronaut, then y is running. Therefore there is at least one x for which y is a mechanic and y is a janitor.
forall x: P(x) -> Q(x). exists x: R(x). forall x: S(x). forall x: R(x) -> P(x). Therefore exists x: S(x) and Q(x).