Translate the following inference to logic notation: There is at least one x for which x_10 is not an astronaut. For all x, x_10 is a bartender if and only if x_10 is a janitor. For all x, x_10 is an astronaut if and only if x_10 is a bartender. Therefore there is at least one x for which x_10 is not a janitor.
exists x: ~P(x). forall x: Q(x) <-> R(x). forall x: P(x) <-> Q(x). Therefore exists x: ~R(x).