Translate the following inference to logic notation: There is at least one x for which if x were happy, then x is running. For all x, if x goes running, then x is happy. Therefore there is at least one x for which if x were happy, then x is running.
exists x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) -> Q(x).