Translate the following inference to logic notation: There is at least one x for which x_8 is a poet if and only if x_8 will go running. For all x, x_8 is a poet or x_8 will not go running. Therefore there is at least one x for which x_8 is a poet if and only if x_8 will go running.
exists x: P(x) <-> Q(x). forall x: P(x) or ~Q(x). Therefore exists x: P(x) <-> Q(x).