Translate the following inference to logic notation: For all x, x_5 will not make tea. For all x, if x_5 plays tennis, then x_5 is making tea. For all x, if x_5 writes a letter, then x_5 is a police officer. For all x, x_5 is a police officer if and only if x_5 will play tennis. Therefore for all x, x_5 will not write a letter.
forall x: ~P(x). forall x: Q(x) -> P(x). forall x: R(x) -> S(x). forall x: S(x) <-> Q(x). Therefore forall x: ~R(x).