Translate the following inference to logic notation: For all x, if x_1 takes a plane, then x_1 is a doctor. For all x, if x_1 were a doctor, then x_1 is taking a plane. If Susan takes a plane, then Susan is a doctor. Therefore Susan is a doctor if and only if Susan is taking a plane.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). P(a) -> Q(a). Therefore Q(a) <-> P(a).