Translate the following inference to logic notation: For all x, x_8 is not bored. For all x, x_8 is bored if and only if x_8 will work. There is at least one x for which x_8 will work or x_8 is not an astronaut. Therefore there is at least one x for which x_8 is not an astronaut.
forall x: ~P(x). forall x: P(x) <-> Q(x). exists x: Q(x) or ~R(x). Therefore exists x: ~R(x).