Translate the following inference to logic notation: For all x, if x_11 were a cashier, then x_11 is a carpenter. There is at least one x for which x_11 is a cashier. For all x, x_11 will play a game if and only if x_11 is a police officer. For all x, if x_11 plays a game, then x_11 is not a carpenter. Therefore there is at least one x for which x_11 is not a police officer.
forall x: P(x) -> Q(x). exists x: P(x). forall x: R(x) <-> S(x). forall x: R(x) -> ~Q(x). Therefore exists x: ~S(x).