Translate the following inference to logic notation: There is at least one x for which y_1 will listen to a song if and only if y_1 is a politician. For all x, if y_1 listens to a song, then y_1 is a politician. Therefore there is at least one x for which if y_1 were a politician, then y_1 is listening to a song.
exists x: P(x) <-> Q(x). forall x: P(x) -> Q(x). Therefore exists x: Q(x) -> P(x).