Translate the following inference to logic notation: For all x, if x_10 were a soldier, then x_10 is playing tennis. There is at least one x for which x_10 is a soldier if and only if x_10 is rich. For all x, x_10 is rich. Therefore there is at least one x for which x_10 will play tennis.
forall x: P(x) -> Q(x). exists x: P(x) <-> R(x). forall x: R(x). Therefore exists x: Q(x).