Translate the following inference to logic notation: For all x, x_9 is sad if and only if x_9 is a politician. For all x, if x_9 were sad, then x_9 is a politician. There is at least one x for which if x_9 were sad, then x_9 is taking a plane. Therefore there is at least one x for which if x_9 were a politician, then x_9 is taking a plane.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). exists x: P(x) -> R(x). Therefore exists x: Q(x) -> R(x).