Translate the following inference to logic notation: For all x, if x takes a plane, then x is a politician. For all x, if x were a politician, then x is a taxi driver. For all x, x will take a plane or x is not a taxi driver. Therefore for all x, x will take a plane if and only if x is a taxi driver.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: P(x) or ~R(x). Therefore forall x: P(x) <-> R(x).