Translate the following inference to logic notation: For all x, x_6 will not play a game. For all x, x_6 will play a game if and only if x_6 will cook. For all x, x_6 is not a nurse or x_6 will listen to a song. There is at least one x for which x_6 is a nurse or x_6 will cook. Therefore there is at least one x for which x_6 will listen to a song.
forall x: ~P(x). forall x: P(x) <-> Q(x). forall x: ~R(x) or S(x). exists x: R(x) or Q(x). Therefore exists x: S(x).