Translate the following inference to logic notation: For all x, x_4 is a scientist if and only if x_4 will take a plane. For all x, x_4 is rich if and only if x_4 is a scientist. There is at least one x for which if x_4 were rich, then x_4 is taking a plane. Therefore there is at least one x for which if x_4 were a scientist, then x_4 is taking a plane.
forall x: P(x) <-> Q(x). forall x: R(x) <-> P(x). exists x: R(x) -> Q(x). Therefore exists x: P(x) -> Q(x).