Translate the following inference to logic notation: For all x, x_7 is a politician if and only if x_7 is rich. For all x, if x_7 were a soldier, then x_7 is a politician. There is at least one x for which x_7 will not take a plane or x_7 is a soldier. For all x, x_7 will take a plane or x_7 is rich. Therefore there is at least one x for which x_7 is a politician.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). exists x: ~S(x) or R(x). forall x: S(x) or Q(x). Therefore exists x: P(x).