Translate the following inference to logic notation: For all x, z_2 will listen to a song if and only if z_2 is a poet. There is at least one x for which z_2 is a poet or z_2 is not a janitor. For all x, z_2 will listen to a song or z_2 is a janitor. Therefore there is at least one x for which z_2 is a poet.
forall x: P(x) <-> Q(x). exists x: Q(x) or ~R(x). forall x: P(x) or R(x). Therefore exists x: Q(x).