Translate the following inference to logic notation: For all x, if x_8 were a bartender, then x_8 is working. For all x, if x_8 were a bartender, then x_8 is not climbing a mountain. For all x, x_8 will climb a mountain. For all x, x_8 will work if and only if x_8 is a bartender. Therefore for all x, x_8 will not work.
forall x: P(x) -> Q(x). forall x: P(x) -> ~R(x). forall x: R(x). forall x: Q(x) <-> P(x). Therefore forall x: ~Q(x).