Translate the following inference to logic notation: For all x, x_10 is sad if and only if x_10 is a doctor. For all x, x_10 is happy if and only if x_10 is sad. There is at least one x for which if x_10 were happy, then x_10 is sad. For all x, x_10 is not a doctor. Therefore there is at least one x for which x_10 is not happy.
forall x: P(x) <-> Q(x). forall x: R(x) <-> P(x). exists x: R(x) -> P(x). forall x: ~Q(x). Therefore exists x: ~R(x).