Translate the following inference to logic notation: It is overcast. Barbara is not taking a plane. For all x, if x_12 listens to a song, then x_12 is taking a plane. For all x, if x_12 takes a plane, then x_12 is listening to a song. Therefore it is overcast and Barbara is not listening to a song.
p. ~P(a). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore p and ~Q(a).