Translate the following inference to logic notation: There is at least one x for which if x were a writer, then x is a police officer. For all x, if x were a politician, then x is taking a plane. For all x, if x were a police officer, then x is a politician. For all x, if x takes a plane, then x is playing a game. Therefore there is at least one x for which if x were a writer, then x is playing a game.
exists x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). forall x: S(x) -> T(x). Therefore exists x: P(x) -> T(x).