Translate the following inference to logic notation: For all x, if z takes a plane, then z is a poet. There is at least one x for which z is not a poet. For all x, z is a poet if and only if z will take a plane. Therefore there is at least one x for which z will not take a plane.
forall x: P(x) -> Q(x). exists x: ~Q(x). forall x: Q(x) <-> P(x). Therefore exists x: ~P(x).