Translate the following inference to logic notation: For all x, z is not a poet. For all x, if x_13 were happy, then x_13 is a janitor. If Thomas were a janitor, then Michael is a poet. For all x, if x_13 were a janitor, then x_13 is happy. Therefore Thomas is not happy.
forall x: ~P(x). forall x: Q(x) -> R(x). R(a) -> P(b). forall x: R(x) -> Q(x). Therefore ~Q(a).