Translate the following inference to logic notation: For all x, if x_10 were a nurse, then x_10 is a mechanic. For all x, if x_10 works, then x_10 is listening to a song. For all x, if x_10 were a mechanic, then x_10 is a nurse. For all x, if x_10 listens to a song, then x_10 is running. For all x, if x_10 were a nurse, then x_10 is working. Therefore for all x, if x_10 were a mechanic, then x_10 is running.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> P(x). forall x: S(x) -> T(x). forall x: P(x) -> R(x). Therefore forall x: Q(x) -> T(x).