Translate the following inference to logic notation: For all x, if x_5 writes a letter, then x_5 is a taxi driver. For all x, if x_5 drinks water, then x_5 is writing a letter. There is at least one x for which if x_5 were a taxi driver, then x_5 is a scientist. For all x, if x_5 were a mechanic, then x_5 is drinking water. Therefore there is at least one x for which if x_5 were a mechanic, then x_5 is a scientist.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> S(x). forall x: T(x) -> R(x). Therefore exists x: T(x) -> S(x).