Translate the following inference to logic notation: For all x, x_8 is happy or x_8 will write a letter. For all x, if x_8 were happy, then x_8 is drinking water. For all x, x_8 will play a game. For all x, x_8 will not drink water. Therefore Patricia is playing a game.
forall x: P(x) or Q(x). forall x: P(x) -> R(x). forall x: S(x). forall x: ~R(x). Therefore S(a).