Translate the following inference to logic notation: For all x, x_7 will play a game or x_7 is a poet. For all x, x_7 is not a writer. There is at least one x for which x_7 is a writer if and only if x_7 is a poet. For all x, x_7 will not play a game or x_7 is an artist. Therefore there is at least one x for which x_7 is an artist.
forall x: P(x) or Q(x). forall x: ~R(x). exists x: R(x) <-> Q(x). forall x: ~P(x) or S(x). Therefore exists x: S(x).