Translate the following inference to logic notation: For all x, if x_5 cooks, then x_5 is listening to a song. For all x, if x_5 were a doctor, then x_5 is poor. For all x, if x_5 listens to a song, then x_5 is a doctor. For all x, x_5 will cook. Therefore for all x, x_5 is poor.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). forall x: P(x). Therefore forall x: S(x).