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