Translate the following inference to logic notation: For all x, x_4 will sleep or x_4 will not go running. There is at least one x for which if x_4 sleeps, then x_4 is running. Therefore there is at least one x for which x_4 will sleep if and only if x_4 will go running.
forall x: P(x) or ~Q(x). exists x: P(x) -> Q(x). Therefore exists x: P(x) <-> Q(x).