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