Translate the following inference to logic notation: For all x, y_3 will listen to a song if and only if y_3 is a police officer. For all x, y_3 will listen to a song or y_3 will write a letter. For all x, y_3 will not go running. For all x, y_3 is a police officer if and only if y_3 will go running. Therefore for all x, y_3 will write a letter.
forall x: P(x) <-> Q(x). forall x: P(x) or R(x). forall x: ~S(x). forall x: Q(x) <-> S(x). Therefore forall x: R(x).