Translate the following inference to logic notation: For all x, x_7 will write a letter if and only if x_7 is a doctor. For all x, if x_7 cooks, then x_7 is playing a game. For all x, if x_7 were a doctor, then x_7 is playing a game. For all x, x_7 will write a letter or x_7 will cook. Therefore for all x, x_7 will play a game.
forall x: P(x) <-> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> S(x). forall x: P(x) or R(x). Therefore forall x: S(x).