Translate the following inference to logic notation: For all x, x_15 is a writer or x_15 will not work. For all x, if x_15 sleeps, then x_15 is playing squash. For all x, if x_15 plays squash, then x_15 is playing a game. There is at least one x for which if x_15 plays a game, then x_15 is working. For all x, if x_15 were a writer, then x_15 is sleeping. Therefore there is at least one x for which x_15 is a writer if and only if x_15 will play squash.
forall x: P(x) or ~Q(x). forall x: R(x) -> S(x). forall x: S(x) -> T(x). exists x: T(x) -> Q(x). forall x: P(x) -> R(x). Therefore exists x: P(x) <-> S(x).