Translate the following inference to logic notation: For all x, if x_14 were a server, then x_14 is a carpenter. For all x, if x_14 were a taxi driver, then x_14 is writing a letter. For all x, if x_14 were a carpenter, then x_14 is a taxi driver. For all x, x_14 is a server or x_14 will not go running. There is at least one x for which if x_14 writes a letter, then x_14 is running. Therefore there is at least one x for which x_14 is a taxi driver if and only if x_14 will write a letter.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). forall x: P(x) or ~T(x). exists x: S(x) -> T(x). Therefore exists x: R(x) <-> S(x).