Translate the following inference to logic notation: For all x, x_13 will drink water. There is at least one x for which x_13 will go running or x_13 will write a letter. For all x, x_13 will take a plane if and only if x_13 will write a letter. For all x, if x_13 goes running, then x_13 is taking a plane. Therefore there is at least one x for which x_13 will drink water and x_13 will take a plane.
forall x: P(x). exists x: Q(x) or R(x). forall x: S(x) <-> R(x). forall x: Q(x) -> S(x). Therefore exists x: P(x) and S(x).