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