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