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