Translate the following inference to logic notation: For all x, if z listens to a song, then z is bored. For all x, z is a poet or z will listen to a song. For all x, z is not a poet or z is a nurse. For all x, if z were bored, then z is listening to a song. There is at least one x for which z will work. For all x, if z were a nurse, then z is bored. Therefore there is at least one x for which z will work and z is bored.
forall x: P(x) -> Q(x). forall x: R(x) or P(x). forall x: ~R(x) or S(x). forall x: Q(x) -> P(x). exists x: T(x). forall x: S(x) -> Q(x). Therefore exists x: T(x) and Q(x).