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