Translate the following inference to logic notation: For all x, x_3 is a mechanic if and only if x_3 is a doctor. There is at least one x for which if x_3 cooks, then x_3 is a lawyer. For all x, if x_3 were a lawyer, then x_3 is a doctor. Therefore there is at least one x for which if x_3 cooks, then x_3 is a mechanic.
forall x: P(x) <-> Q(x). exists x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore exists x: R(x) -> P(x).