Translate the following inference to logic notation: For all x, if x_8 plays a game, then x_8 is writing a letter. For all x, x_8 will play squash if and only if x_8 will play a game. For all x, x_8 will not climb a mountain or x_8 is an artist. There is at least one x for which x_8 will climb a mountain or x_8 will play squash. For all x, x_8 will not write a letter. Therefore there is at least one x for which x_8 is an artist.
forall x: P(x) -> Q(x). forall x: R(x) <-> P(x). forall x: ~S(x) or T(x). exists x: S(x) or R(x). forall x: ~Q(x). Therefore exists x: T(x).