Translate the following inference to logic notation: There is at least one x for which x_5 is a janitor. For all x, x_5 will not play squash. For all x, if x_5 were a janitor, then x_5 is playing squash. Therefore there is at least one x for which x_5 will write a letter.
exists x: P(x). forall x: ~Q(x). forall x: P(x) -> Q(x). Therefore exists x: R(x).