Translate the following inference to logic notation: For all x, if x_8 were a scientist, then x_8 is playing a game. There is at least one x for which x_8 will go running. For all x, x_8 will play a game if and only if x_8 is rich. For all x, x_8 is a scientist or x_8 is rich. Therefore there is at least one x for which x_8 will play a game and x_8 will go running.
forall x: P(x) -> Q(x). exists x: R(x). forall x: Q(x) <-> S(x). forall x: P(x) or S(x). Therefore exists x: Q(x) and R(x).