Translate the following inference to logic notation: For all x, x_7 will go running or x_7 is not a soldier. There is at least one x for which x_7 is a soldier if and only if x_7 will go running. Therefore there is at least one x for which x_7 will go running if and only if x_7 is a soldier.
forall x: P(x) or ~Q(x). exists x: Q(x) <-> P(x). Therefore exists x: P(x) <-> Q(x).