Translate the following inference to logic notation: For all x, z is excited if and only if z will take a plane. There is at least one x for which if z were excited, then z is taking a plane. Therefore there is at least one x for which if z takes a plane, then z is excited.
forall x: P(x) <-> Q(x). exists x: P(x) -> Q(x). Therefore exists x: Q(x) -> P(x).