Translate the following inference to logic notation: For all x, x_6 will not go running. For all x, x_6 is a nurse if and only if x_6 will go running. There is at least one x for which x_6 will listen to a song or x_6 is a nurse. For all x, x_6 will not listen to a song or x_6 is excited. Therefore there is at least one x for which x_6 is excited.
forall x: ~P(x). forall x: Q(x) <-> P(x). exists x: R(x) or Q(x). forall x: ~R(x) or S(x). Therefore exists x: S(x).