Translate the following inference to logic notation: For all x, x_3 is a doctor if and only if x_3 is happy. For all x, if x_3 sleeps, then x_3 is happy. There is at least one x for which x_3 will sleep or x_3 is a doctor. Therefore there is at least one x for which x_3 is happy.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). exists x: R(x) or P(x). Therefore exists x: Q(x).