Translate the following inference to logic notation: For all x, if x_6 were a poet, then x_6 is drinking water. For all x, if x_6 were poor, then x_6 is a poet. There is at least one x for which if x_6 drinks water, then x_6 is a carpenter. For all x, if x_6 were a carpenter, then x_6 is poor. Therefore there is at least one x for which x_6 is a poet if and only if x_6 will drink water.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> S(x). forall x: S(x) -> R(x). Therefore exists x: P(x) <-> Q(x).