Translate the following inference to logic notation: For all x, if x_5 cooks, then x_5 is a writer. For all x, if x_5 cooks, then x_5 is a writer. For all x, if x_5 were a writer, then x_5 is cooking. Therefore for all x, x_5 will cook if and only if x_5 is a writer.
forall x: P(x) -> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).