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