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