Translate the following inference to logic notation: For all x, z is excited if and only if z will drink water. For all x, z is excited if and only if z will make tea. For all x, if z drinks water, then z is making tea. Therefore for all x, z is excited if and only if z will make tea.
forall x: P(x) <-> Q(x). forall x: P(x) <-> R(x). forall x: Q(x) -> R(x). Therefore forall x: P(x) <-> R(x).