Translate the following inference to logic notation: For all x, if x_14 cooks, then x_14 is a taxi driver. For all x, x_14 is not a taxi driver. If Barbara climbs a mountain, then John is cooking. For all x, x_14 will cook if and only if x_14 is a taxi driver. Therefore Barbara is not climbing a mountain.
forall x: P(x) -> Q(x). forall x: ~Q(x). p -> P(a). forall x: P(x) <-> Q(x). Therefore ~p.