Translate the following inference to logic notation: For all x, if x_11 plays a game, then x_11 is curious. For all x, if x_11 cooks, then x_11 is playing a game. There is at least one x for which if x_11 were a writer, then x_11 is cooking. For all x, x_11 is a writer or x_11 is not curious. Therefore there is at least one x for which x_11 will play a game if and only if x_11 will cook.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: S(x) -> R(x). forall x: S(x) or ~Q(x). Therefore exists x: P(x) <-> R(x).