Translate the following inference to logic notation: For all x, x_7 is rich if and only if x_7 will play tennis. There is at least one x for which if x_7 were a bartender, then x_7 is playing tennis. For all x, if x_7 were an astronaut, then x_7 is rich. For all x, x_7 is an astronaut or x_7 is a bartender. Therefore there is at least one x for which x_7 will play tennis.
forall x: P(x) <-> Q(x). exists x: R(x) -> Q(x). forall x: S(x) -> P(x). forall x: S(x) or R(x). Therefore exists x: Q(x).