Translate the following inference to logic notation: For all x, if z_2 were an office clerk, then z_2 is reading a book. For all x, if z_2 reads a book, then z_2 is a server. For all x, if z_2 were a server, then z_2 is playing squash. There is at least one x for which if z_2 plays squash, then z_2 is a janitor. Therefore there is at least one x for which if z_2 were an office clerk, then z_2 is a janitor.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). exists x: S(x) -> T(x). Therefore exists x: P(x) -> T(x).