Translate the following inference to logic notation: For all x, x_15 will play tennis. For all x, if x_15 plays tennis, then x_15 is a politician. There is at least one x for which if x_15 were a politician, then x_15 is happy. For all x, x_15 is a janitor if and only if x_15 is happy. Therefore there is at least one x for which x_15 is a janitor.
forall x: P(x). forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: S(x) <-> R(x). Therefore exists x: S(x).