Translate the following inference to logic notation: For all x, x_2 will take a plane if and only if x_2 is a server. For all x, x_2 is happy if and only if x_2 is a server. There is at least one x for which if x_2 were a server, then x_2 is happy. Therefore there is at least one x for which if x_2 were happy, then x_2 is taking a plane.
forall x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). exists x: Q(x) -> R(x). Therefore exists x: R(x) -> P(x).