Translate the following inference to logic notation: There is at least one x for which y will go running if and only if y is happy. For all x, y will work if and only if y is happy. Therefore there is at least one x for which if y works, then y is running.
exists x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). Therefore exists x: R(x) -> P(x).