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