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