Translate the following inference to logic notation: For all x, y will sleep if and only if y will go running. For all x, y will go running or y will not sleep. Therefore for all x, y will go running if and only if y will sleep.
forall x: P(x) <-> Q(x). forall x: Q(x) or ~P(x). Therefore forall x: Q(x) <-> P(x).