Translate the following inference to logic notation: For all x, z will make tea if and only if x_11 is a server. For all x, x_11 is a server. For all x, if x_11 listens to a song, then z is making tea. Therefore there is at least one x for which z will make tea.
forall x: P(x) <-> Q(x). forall x: Q(x). forall x: R(x) -> P(x). Therefore exists x: P(x).