Translate the following inference to logic notation: For all x, if x_7 were a soldier, then x_7 is playing tennis. For all x, x_7 is a soldier. There is at least one x for which if x_7 plays tennis, then x_7 is a soldier. Therefore there is at least one x for which x_7 will play tennis.
forall x: P(x) -> Q(x). forall x: P(x). exists x: Q(x) -> P(x). Therefore exists x: Q(x).