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