Translate the following inference to logic notation: For all x, x_8 is a scientist if and only if x_8 is a lawyer. For all x, x_8 is not a scientist. There is at least one x for which x_8 is a lawyer if and only if x_8 is excited. Therefore there is at least one x for which x_8 is not excited.
forall x: P(x) <-> Q(x). forall x: ~P(x). exists x: Q(x) <-> R(x). Therefore exists x: ~R(x).