Translate the following inference to logic notation: For all x, x_8 will drink water or x_8 is not a janitor. There is at least one x for which x_8 is bored. For all x, x_8 is a carpenter. For all x, if x_8 were a carpenter, then x_8 is drinking water. Therefore there is at least one x for which x_8 will drink water and x_8 is bored.
forall x: P(x) or ~Q(x). exists x: R(x). forall x: S(x). forall x: S(x) -> P(x). Therefore exists x: P(x) and R(x).