Translate the following inference to logic notation: For all x, if y were sad, then y is a writer. For all x, if y were a writer, then y is sad. For all x, y is sad if and only if y is a writer. Therefore for all x, y is sad if and only if y is a writer.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) <-> Q(x). Therefore forall x: P(x) <-> Q(x).