Translate the following inference to logic notation: For all x, x_4 is a nurse if and only if x_4 will listen to a song. There is at least one x for which x_4 will listen to a song. Therefore there is at least one x for which x_4 is a nurse.
forall x: P(x) <-> Q(x). exists x: Q(x). Therefore exists x: P(x).