Translate the following inference to logic notation: For all x, x_2 will write a letter or x_2 is a politician. For all x, x_2 will write a letter if and only if x_2 is a server. There is at least one x for which x_2 is an astronaut. For all x, x_2 is not a server. Therefore there is at least one x for which x_2 is an astronaut and x_2 is a politician.
forall x: P(x) or Q(x). forall x: P(x) <-> R(x). exists x: S(x). forall x: ~R(x). Therefore exists x: S(x) and Q(x).