Translate the following inference to logic notation: For all x, if x_12 listens to a song, then x_12 is working. For all x, if x_12 listens to a song, then x_12 is not cooking. For all x, x_12 will work if and only if x_12 will listen to a song. For all x, x_12 will cook and x_12 is a bartender. Therefore for all x, x_12 will not work.
forall x: P(x) -> Q(x). forall x: P(x) -> ~R(x). forall x: Q(x) <-> P(x). forall x: R(x) and S(x). Therefore forall x: ~Q(x).