Translate the following inference to logic notation: There is at least one x for which if y_1 listens to a song, then y_1 is playing a game. For all x, if y_1 were sad, then y_1 is listening to a song. For all x, y_1 will not play a game. For all x, if y_1 were a sailor, then y_1 is sad. Therefore there is at least one x for which y_1 is not a sailor.
exists x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: ~Q(x). forall x: S(x) -> R(x). Therefore exists x: ~S(x).