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