Translate the following inference to logic notation: For all x, if x_5 plays squash, then x_5 is working. For all x, if x_5 works, then x_5 is an astronaut. For all x, x_5 will play squash if and only if x_5 is an astronaut. Therefore for all x, x_5 will play squash if and only if x_5 is an astronaut.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: P(x) <-> R(x). Therefore forall x: P(x) <-> R(x).