Translate the following inference to logic notation: For all x, x_18 is not fast. For all x, x_18 will play a game or x_18 is rich. There is at least one x for which x_18 will play a game if and only if x_18 is fast. For all x, x_18 is bored. Therefore there is at least one x for which x_18 is bored.
forall x: ~P(x). forall x: Q(x) or R(x). exists x: Q(x) <-> P(x). forall x: S(x). Therefore exists x: S(x).