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