Translate the following inference to logic notation: For all x, if x_8 writes a letter, then x_8 is a doctor. Jessica is not a bartender. For all x, if x_8 were a doctor, then x_8 is writing a letter. William is writing a letter if and only if Jessica is a bartender. Therefore William is not a doctor.
forall x: P(x) -> Q(x). ~p. forall x: Q(x) -> P(x). P(a) <-> p. Therefore ~Q(a).