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