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