Translate the following inference to logic notation: For all x, x is a soldier if and only if x will play tennis. For all x, x is a soldier or x will not play tennis. For all x, if x plays tennis, then x is a soldier. Therefore for all x, x is a soldier if and only if x will play tennis.
forall x: P(x) <-> Q(x). forall x: P(x) or ~Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).