Translate the following inference to logic notation: For all x, if z cooks, then z is making tea. For all x, if z makes tea, then z is cooking. For all x, z will make tea if and only if z will cook. Therefore for all x, z will cook if and only if z will make tea.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) <-> P(x). Therefore forall x: P(x) <-> Q(x).