Translate the following inference to logic notation: There is at least one x for which x_9 is a carpenter if and only if x_9 is a janitor. For all x, x_9 is a janitor or x_9 is not a poet. For all x, x_9 is not a carpenter. Therefore there is at least one x for which x_9 is not a poet.
exists x: P(x) <-> Q(x). forall x: Q(x) or ~R(x). forall x: ~P(x). Therefore exists x: ~R(x).