Translate the following inference to logic notation: For all x, if z_1 were an office clerk, then z_1 is listening to a song. There is at least one x for which z_1 is an office clerk or z_1 will not listen to a song. Therefore there is at least one x for which if z_1 listens to a song, then z_1 is an office clerk.
forall x: P(x) -> Q(x). exists x: P(x) or ~Q(x). Therefore exists x: Q(x) -> P(x).