Translate the following inference to logic notation: For all x, if x_8 makes tea, then x_8 is playing tennis. For all x, if x_8 were happy, then x_8 is sad. There is at least one x for which if x_8 plays tennis, then x_8 is sad. For all x, x_8 will not write a letter or x_8 is happy. For all x, x_8 will write a letter. Therefore there is at least one x for which x_8 is sad.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: Q(x) -> S(x). forall x: ~T(x) or R(x). forall x: T(x). Therefore exists x: S(x).