Translate the following inference to logic notation: For all x, x_8 will play squash if and only if x_8 is sad. There is at least one x for which if x_8 were poor, then x_8 is an astronaut. For all x, if x_8 plays squash, then x_8 is poor. Therefore there is at least one x for which if x_8 were sad, then x_8 is an astronaut.
forall x: P(x) <-> Q(x). exists x: R(x) -> S(x). forall x: P(x) -> R(x). Therefore exists x: Q(x) -> S(x).