Translate the following inference to logic notation: There is at least one x for which x_11 will take a plane if and only if x_11 will go running. For all x, x_11 will take a plane or x_11 is not a lawyer. For all x, if x_11 goes running, then x_11 is a lawyer. Therefore there is at least one x for which x_11 will go running if and only if x_11 will take a plane.
exists x: P(x) <-> Q(x). forall x: P(x) or ~R(x). forall x: Q(x) -> R(x). Therefore exists x: Q(x) <-> P(x).