Translate the following inference to logic notation: There is at least one x for which x_7 will listen to a song if and only if x_7 will take a plane. For all x, x_7 will take a plane or x_7 will not listen to a song. Therefore there is at least one x for which x_7 will take a plane if and only if x_7 will listen to a song.
exists x: P(x) <-> Q(x). forall x: Q(x) or ~P(x). Therefore exists x: Q(x) <-> P(x).