Translate the following inference to logic notation: For all x, x_11 is not poor. For all x, x_11 will play tennis if and only if x_11 is poor. There is at least one x for which x_11 will play tennis. For all x, if x_11 were poor, then x_11 is playing tennis. Therefore there is at least one x for which x_11 is an astronaut.
forall x: ~P(x). forall x: Q(x) <-> P(x). exists x: Q(x). forall x: P(x) -> Q(x). Therefore exists x: R(x).