Translate the following inference to logic notation: For all x, x is a poet. For all x, x is a carpenter or x is not happy. For all x, x is happy. Therefore for all x, x is a carpenter and x is a poet.
forall x: P(x). forall x: Q(x) or ~R(x). forall x: R(x). Therefore forall x: Q(x) and P(x).