pls show work and explain if you could

Exercise 2.26 Consider languages over a fixed alphabet with S 2. Answer true or false to the following questions. Justify your answers, giving examples of the languages Li and L2 where appropriate. a) If Liis nonregular and L SL, then Ly is nonregular, b) If I SL, and L2 is nonregular, then Lis nonregular, c) If Liis nonregular, then its complement Li is nonregular, d) If L is regular, then LUL, is regular for any language L2, e) If L and L, are nonregular, then L L is nonregular