Translate the following inference to logic notation: For all x, if x_1 were rich, then x_1 is taking a plane. For all x, if x_1 were happy, then x_1 is taking a plane. For all x, x_1 will write a letter or x_1 is rich. There is at least one x for which if x_1 writes a letter, then x_1 is happy. Therefore there is at least one x for which x_1 will take a plane.
forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: S(x) or P(x). exists x: S(x) -> R(x). Therefore exists x: Q(x).