Translate the following inference to logic notation: For all x, if x_5 were a mechanic, then x_5 is a police officer. There is at least one x for which x_5 is not a police officer. For all x, if x_5 were a police officer, then x_5 is a mechanic. Therefore there is at least one x for which x_5 is not a mechanic.
forall x: P(x) -> Q(x). exists x: ~Q(x). forall x: Q(x) -> P(x). Therefore exists x: ~P(x).