Translate the following inference to logic notation: There is at least one x for which y is not excited. For all x, y is excited if and only if y is a doctor. For all x, y is a janitor if and only if y is a doctor. Therefore there is at least one x for which y is not a janitor.
exists x: ~P(x). forall x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). Therefore exists x: ~R(x).