Translate the following inference to logic notation: For all x, if x_5 were a taxi driver, then x_5 is taking a plane. There is at least one x for which x_5 is sad if and only if x_5 is a taxi driver. For all x, x_5 will not climb a mountain. For all x, if x_5 takes a plane, then x_5 is climbing a mountain. Therefore there is at least one x for which x_5 is not sad.
forall x: P(x) -> Q(x). exists x: R(x) <-> P(x). forall x: ~S(x). forall x: Q(x) -> S(x). Therefore exists x: ~R(x).