Translate the following inference to logic notation: For all x, x_3 is a politician or x_3 is a police officer. For all x, x_3 is a police officer if and only if x_3 will write a letter. There is at least one x for which if x_3 were a politician, then x_3 is writing a letter. Therefore there is at least one x for which x_3 will write a letter.
forall x: P(x) or Q(x). forall x: Q(x) <-> R(x). exists x: P(x) -> R(x). Therefore exists x: R(x).