Translate the following inference to logic notation: For all x, x_5 will play a game or x_5 will make tea. For all x, if x_5 plays a game, then x_5 is writing a letter. There is at least one x for which if x_5 makes tea, then x_5 is writing a letter. For all x, if x_5 writes a letter, then x_5 is playing a game. Therefore there is at least one x for which x_5 will write a letter.
forall x: P(x) or Q(x). forall x: P(x) -> R(x). exists x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: R(x).