Translate the following inference to logic notation: For all x, y will work if and only if y will listen to a song. For all x, y will not work. For all x, if y were an office clerk, then y is a doctor. For all x, if y were a doctor, then y is listening to a song. For all x, if y listens to a song, then y is an office clerk. Therefore for all x, y is not an office clerk.
forall x: P(x) <-> Q(x). forall x: ~P(x). forall x: R(x) -> S(x). forall x: S(x) -> Q(x). forall x: Q(x) -> R(x). Therefore forall x: ~R(x).