Translate the following inference to logic notation: For all x, x_9 will take a plane or x_9 will not make tea. For all x, if x_9 makes tea, then x_9 is taking a plane. For all x, if x_9 takes a plane, then x_9 is making tea. Therefore for all x, x_9 will take a plane if and only if x_9 will make tea.
forall x: P(x) or ~Q(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore forall x: P(x) <-> Q(x).