Translate the following inference to logic notation: There is at least one x for which if x_10 were rich, then x_10 is taking a plane. For all x, if x_10 were happy, then x_10 is taking a plane. For all x, if x_10 plays a game, then x_10 is happy. For all x, x_10 will play a game or x_10 will not write a letter. For all x, x_10 is rich or x_10 will write a letter. Therefore there is at least one x for which x_10 will take a plane.
exists x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: S(x) -> R(x). forall x: S(x) or ~T(x). forall x: P(x) or T(x). Therefore exists x: Q(x).