Translate the following inference to logic notation: For all x, x_12 is excited or x_12 will take a plane. For all x, if x_12 were a lawyer, then x_12 is listening to a song. For all x, x_12 is a lawyer if and only if x_12 will take a plane. For all x, x_12 is excited if and only if x_12 will listen to a song. Therefore for all x, x_12 will listen to a song.
forall x: P(x) or Q(x). forall x: R(x) -> S(x). forall x: R(x) <-> Q(x). forall x: P(x) <-> S(x). Therefore forall x: S(x).