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