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