Translate the following inference to logic notation: For all x, if x_10 were sad, then x_10 is excited. For all x, x_10 will not sleep. There is at least one x for which if x_10 were excited, then x_10 is not a lawyer. For all x, x_10 will sleep or x_10 is a lawyer. Therefore there is at least one x for which x_10 is not sad.
forall x: P(x) -> Q(x). forall x: ~R(x). exists x: Q(x) -> ~S(x). forall x: R(x) or S(x). Therefore exists x: ~P(x).