Translate the following inference to logic notation: For all x, if x_7 writes a letter, then x_7 is a police officer. There is at least one x for which if x_7 were a police officer, then x_7 is writing a letter. For all x, x_7 is not a police officer. For all x, if x_7 were a police officer, then x_7 is writing a letter. Therefore there is at least one x for which x_7 will not write a letter.
forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). forall x: ~Q(x). forall x: Q(x) -> P(x). Therefore exists x: ~P(x).