Translate the following inference to logic notation: Barbara is not poor. For all x, x_22 will listen to a song if and only if x_22 is poor. Mary is not fast. For all x, y_3 is an astronaut if and only if y_3 is fast. Therefore Mary is not an astronaut and Barbara is not listening to a song.
~P(a). forall x: Q(x) <-> P(x). ~R(b). forall x: S(x) <-> R(x). Therefore ~S(b) and ~Q(a).