Translate the following inference to logic notation: There is at least one x for which x_12 will work or x_12 is not a poet. For all x, if x_12 works, then x_12 is a poet. For all x, if x_12 were a poet, then x_12 is working. Therefore there is at least one x for which if x_12 were a poet, then x_12 is working.
exists x: P(x) or ~Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore exists x: Q(x) -> P(x).