Translate the following inference to logic notation: For all x, x_7 will sleep if and only if x_7 will go running. For all x, x_7 will not sleep. For all x, x_7 will play tennis if and only if x_7 will go running. There is at least one x for which if x_7 were fast, then x_7 is playing tennis. Therefore there is at least one x for which x_7 is not fast.
forall x: P(x) <-> Q(x). forall x: ~P(x). forall x: R(x) <-> Q(x). exists x: S(x) -> R(x). Therefore exists x: ~S(x).