Translate the following inference to logic notation: For all x, if z were a writer, then z is an electrician. For all x, if z were an electrician, then z is drinking water. There is at least one x for which if z were rich, then z is a writer. For all x, if z drinks water, then z is writing a letter. Therefore there is at least one x for which if z were rich, then z is writing a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: S(x) -> P(x). forall x: R(x) -> T(x). Therefore exists x: S(x) -> T(x).