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