Translate the following inference to logic notation: For all x, x_10 will play tennis if and only if x_10 will cook. There is at least one x for which if x_10 plays tennis, then x_10 is writing a letter. For all x, if x_10 cooks, then x_10 is a soldier. For all x, if x_10 writes a letter, then x_10 is playing tennis. For all x, x_10 is not a soldier. Therefore there is at least one x for which x_10 will not write a letter.
forall x: P(x) <-> Q(x). exists x: P(x) -> R(x). forall x: Q(x) -> S(x). forall x: R(x) -> P(x). forall x: ~S(x). Therefore exists x: ~R(x).