Translate the following inference to logic notation: For all x, if z_2 plays tennis, then z_2 is taking a plane. For all x, z_2 will play tennis or z_2 will not take a plane. For all x, if z_2 takes a plane, then z_2 is playing tennis. Therefore for all x, z_2 will play tennis if and only if z_2 will take a plane.
forall x: P(x) -> Q(x). forall x: P(x) or ~Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).