h Prove that, for an arbitrarily given short exact sequence 0 - X- ry_*_2- +20 of modules over R together with arbitrarily given projective resolu- tions C and E of the modules X and 2, respectively, there exists a projective resolution D of the module Y and two chain transformations f: CD, :D E of these lower sequences such that, for every n>0, 8: gn Cn En 0- Dn --0 is a short exact sequence which splits. State and prove the dual result for injective resolutions. h Prove that, for an arbitrarily given short exact sequence 0 - X- ry_*_2- +20 of modules over R together with arbitrarily given projective resolu- tions C and E of the modules X and 2, respectively, there exists a projective resolution D of the module Y and two chain transformations f: CD, :D E of these lower sequences such that, for every n>0, 8: gn Cn En 0- Dn --0 is a short exact sequence which splits. State and prove the dual result for injective resolutions