Translate the following inference to logic notation: For all x, if x_9 makes tea, then x_9 is playing squash. For all x, x_9 will make tea if and only if x_9 will play squash. For all x, if x_9 plays squash, then x_9 is making tea. Therefore for all x, x_9 will play squash if and only if x_9 will make tea.
forall x: P(x) -> Q(x). forall x: P(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).