Translate the following inference to logic notation: For all x, if x_5 makes tea, then x_5 is an astronaut. For all x, x_5 will work or x_5 will make tea. For all x, if x_5 works, then x_5 is a carpenter. For all x, if x_5 were a carpenter, then x_5 is an astronaut. Therefore for all x, x_5 is an astronaut or x_5 will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) or P(x). forall x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore forall x: Q(x) or T(x).