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