Translate the following inference to logic notation: For all x, x_11 is rich or x_11 will cook. For all x, x_11 will cook if and only if x_11 will listen to a song. There is at least one x for which x_11 is a carpenter. For all x, if x_11 listens to a song, then x_11 is working. For all x, if x_11 were rich, then x_11 is listening to a song. Therefore there is at least one x for which x_11 is a carpenter and x_11 will work.
forall x: P(x) or Q(x). forall x: Q(x) <-> R(x). exists x: S(x). forall x: R(x) -> T(x). forall x: P(x) -> R(x). Therefore exists x: S(x) and T(x).