Translate the following inference to logic notation: For all x, if x_5 were a soldier, then x_5 is happy. For all x, x_5 will play squash or x_5 is an astronaut. For all x, if x_5 were an astronaut, then x_5 is happy. For all x, x_5 will listen to a song. For all x, if x_5 plays squash, then x_5 is a soldier. Therefore for all x, x_5 will listen to a song and x_5 is happy.
forall x: P(x) -> Q(x). forall x: R(x) or S(x). forall x: S(x) -> Q(x). forall x: T(x). forall x: R(x) -> P(x). Therefore forall x: T(x) and Q(x).