Translate the following inference to logic notation: For all x, if x_7 were a poet, then x_7 is a writer. There is at least one x for which if x_7 were excited, then x_7 is a poet. For all x, x_7 is a writer if and only if x_7 is excited. Therefore there is at least one x for which if x_7 were a writer, then x_7 is excited.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: Q(x) <-> R(x). Therefore exists x: Q(x) -> R(x).