Translate the following inference to logic notation: For all x, x_1 will not take a plane. For all x, if x_1 were a server, then x_1 is taking a plane. There is at least one x for which x_1 will listen to a song if and only if x_1 is a server. Therefore there is at least one x for which x_1 will not listen to a song.
forall x: ~P(x). forall x: Q(x) -> P(x). exists x: R(x) <-> Q(x). Therefore exists x: ~R(x).