Translate the following inference to logic notation: Barbara is a bartender if and only if it is cloudy. For all x, x_8 will work if and only if x_8 is a bartender. For all x, x_8 will not work. Therefore it is not cloudy.
P(a) <-> p. forall x: Q(x) <-> P(x). forall x: ~Q(x). Therefore ~p.