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