Translate the following inference to logic notation: For all x, z_1 will drink water or z_1 will not listen to a song. For all x, z_1 will drink water if and only if z_1 will work. There is at least one x for which z_1 will work or z_1 will listen to a song. Therefore there is at least one x for which z_1 will drink water.
forall x: P(x) or ~Q(x). forall x: P(x) <-> R(x). exists x: R(x) or Q(x). Therefore exists x: P(x).