Translate the following inference to logic notation: For all x, x_10 is a cashier. For all x, if x_10 listens to a song, then x_10 is a server. For all x, if x_10 were sad, then x_10 is not a cashier. For all x, if x_10 were a server, then x_10 is a carpenter. For all x, x_10 is sad if and only if x_10 is a server. For all x, if x_10 were a carpenter, then x_10 is listening to a song. Therefore for all x, x_10 will not listen to a song.
forall x: P(x). forall x: Q(x) -> R(x). forall x: S(x) -> ~P(x). forall x: R(x) -> T(x). forall x: S(x) <-> R(x). forall x: T(x) -> Q(x). Therefore forall x: ~Q(x).