Translate the following inference to logic notation: For all x, x_4 is not a carpenter. For all x, x_4 is a doctor or x_4 will play a game. For all x, x_4 is a doctor if and only if x_4 is a carpenter. Therefore for all x, x_4 will play a game.
forall x: ~P(x). forall x: Q(x) or R(x). forall x: Q(x) <-> P(x). Therefore forall x: R(x).