Translate the following inference to logic notation: For all x, if x_8 makes tea, then x_8 is writing a letter. For all x, if x_8 were sad, then x_8 is excited. For all x, if x_8 were excited, then x_8 is making tea. For all x, if x_8 writes a letter, then x_8 is sad. Therefore if William were sad, then William is excited.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: S(x) -> P(x). forall x: Q(x) -> R(x). Therefore R(a) -> S(a).