Translate the following inference to logic notation: There is at least one x for which if x_4 were an electrician, then x_4 is listening to a song. For all x, x_4 will listen to a song. For all x, if x_4 listens to a song, then x_4 is an electrician. Therefore there is at least one x for which x_4 is an electrician.
exists x: P(x) -> Q(x). forall x: Q(x). forall x: Q(x) -> P(x). Therefore exists x: P(x).