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