Translate the following inference to logic notation: For all x, x_13 will play a game if and only if x_13 is sad. There is at least one x for which x_13 is sad. For all x, x_13 is fast. Therefore there is at least one x for which x_13 is fast and x_13 will play a game.
forall x: P(x) <-> Q(x). exists x: Q(x). forall x: R(x). Therefore exists x: R(x) and P(x).