Translate the following inference to logic notation: For all x, x_2 is not sad. There is at least one x for which x_2 will play a game or x_2 is sad. For all x, x_2 will not play a game or x_2 will write a letter. Therefore there is at least one x for which x_2 will write a letter.
forall x: ~P(x). exists x: Q(x) or P(x). forall x: ~Q(x) or R(x). Therefore exists x: R(x).