Problem #5 (30 points) Prove the following with the method indicated: a) (AUB) CUB=BAC using set identities. b) An(B-C)=( AB)-( AC)using membership tables. c) AU ( AB) = A using Venn diagrams. Problem #6 (15 points) Let X = {1, 2, 3}, Y = {1, 2, 3, 4). and Z = {1, 2}. Using arrow diagrams, define the functions below. In each case provide a small comment explaining why the required property is true or false. a) Define a function fi: X Y that is one-to-one but not onto. b) Define a function : X-Z that is onto but not one-to-one. c) Define a function f3: XXthat is neither one-to-one nor onto. d) Define a function f4 X X that is one-to-one and onto but is not the identity function on X