Translate the following inference to logic notation: For all x, z_1 is a nurse if and only if z_1 will take a plane. There is at least one x for which z_1 is a cashier or z_1 is not a nurse. For all x, if z_1 were a cashier, then z_1 is taking a plane. Therefore there is at least one x for which z_1 will take a plane if and only if z_1 is a nurse.
forall x: P(x) <-> Q(x). exists x: R(x) or ~P(x). forall x: R(x) -> Q(x). Therefore exists x: Q(x) <-> P(x).