Translate the following inference to logic notation: There is at least one x for which x_2 will drink water if and only if x_2 is a poet. For all x, x_2 is a poet if and only if x_2 will drink water. For all x, if x_2 were a poet, then x_2 is drinking water. Therefore there is at least one x for which x_2 will drink water if and only if x_2 is a poet.
exists x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) <-> Q(x).