Translate the following inference to logic notation: For all x, if x_9 were a poet, then x_9 is writing a letter. For all x, x_9 is a poet or x_9 will not write a letter. There is at least one x for which if x_9 were a poet, then x_9 is writing a letter. Therefore there is at least one x for which if x_9 writes a letter, then x_9 is a poet.
forall x: P(x) -> Q(x). forall x: P(x) or ~Q(x). exists x: P(x) -> Q(x). Therefore exists x: Q(x) -> P(x).