Translate the following inference to logic notation: For all x, x_10 will climb a mountain if and only if x_10 will write a letter. For all x, if x_10 writes a letter, then x_10 is taking a plane. For all x, if x_10 goes running, then x_10 is writing a letter. For all x, if x_10 takes a plane, then x_10 is running. There is at least one x for which x_10 will not take a plane. Therefore there is at least one x for which x_10 will not climb a mountain.
forall x: P(x) <-> Q(x). forall x: Q(x) -> R(x). forall x: S(x) -> Q(x). forall x: R(x) -> S(x). exists x: ~R(x). Therefore exists x: ~P(x).