Translate the following inference to logic notation: For all x, x_8 is a bartender or x_8 will write a letter. For all x, x_8 is not a sailor. For all x, x_8 will cook if and only if x_8 is a sailor. For all x, if x_8 were a bartender, then x_8 is cooking. Therefore for all x, x_8 will write a letter.
forall x: P(x) or Q(x). forall x: ~R(x). forall x: S(x) <-> R(x). forall x: P(x) -> S(x). Therefore forall x: Q(x).