Translate the following inference to logic notation: For all x, if x_7 works, then x_7 is a sailor. There is at least one x for which if x_7 were a sailor, then x_7 is a writer. For all x, x_7 will play a game. For all x, if x_7 were a writer, then x_7 is not playing a game. Therefore there is at least one x for which x_7 will not work.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: S(x). forall x: R(x) -> ~S(x). Therefore exists x: ~P(x).