Translate the following inference to logic notation: For all x, x_13 is not an astronaut. There is at least one x for which x_13 will work. For all x, x_13 is an astronaut or x_13 will make tea. Therefore there is at least one x for which x_13 will work or x_13 is a politician.
forall x: ~P(x). exists x: Q(x). forall x: P(x) or R(x). Therefore exists x: Q(x) or S(x).