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