Translate the following inference to logic notation: For all x, x_5 is an artist if and only if x_5 will write a letter. For all x, if x_5 plays a game, then x_5 is writing a letter. For all x, if x_5 were sad, then x_5 is playing a game. For all x, x_5 is an artist or x_5 is sad. Therefore for all x, x_5 will write a letter.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). forall x: S(x) -> R(x). forall x: P(x) or S(x). Therefore forall x: Q(x).