Translate the following inference to logic notation: For all x, x is a mechanic or x will not sleep. For all x, x will sleep. There is at least one x for which if x were a mechanic, then x is fast. Therefore there is at least one x for which x is fast.
forall x: P(x) or ~Q(x). forall x: Q(x). exists x: P(x) -> R(x). Therefore exists x: R(x).