Translate the following inference to logic notation: For all x, x_11 will play a game if and only if x_11 will play tennis. There is at least one x for which x_11 will cook if and only if x_11 will play tennis. For all x, x_11 will not cook. Therefore there is at least one x for which x_11 will not play a game.
forall x: P(x) <-> Q(x). exists x: R(x) <-> Q(x). forall x: ~R(x). Therefore exists x: ~P(x).