10. (20) For each of the following statements, state whether it is TRUE or FALSE. Prove your answer

a = = = a = - (a) For any L1, L2, L1 = L2 iff Li = L. (b) ( U*) n (0 (*)) = 0. (c) Every infinite language is the complement of a finite language. (d) For any Lil, L2, (L1L2)* = Lil. (e) For any L1, L2, (L1 U L2)* = Li UL. (f) For any L1, L2, L3, (L1 U L2)L3 = L1L3 U L2L3. U (g) For any L1, L2, L3, (L1L2) U L3) = (Lj U L3)(L2 U L3). (h) For any L, (L+)* = L*. . (i) For any L, L* = {f}. . (j) For any L, UL+ = L*. = = = = =