Translate the following inference to logic notation: There is at least one x for which x_6 is not happy. For all x, x_6 is happy if and only if x_6 is a lawyer. For all x, x_6 is a lawyer if and only if x_6 is a carpenter. Therefore there is at least one x for which x_6 is not a carpenter.
exists x: ~P(x). forall x: P(x) <-> Q(x). forall x: Q(x) <-> R(x). Therefore exists x: ~R(x).