6. Decide whether each statement below is true or false. If it is true, prove it. If not, give a counterexample. The alphabet is sa, b. (a) If Ci S L2 and is not regular, then L is not regular. (b) I L2 and L is not regular, then L is not regular. (c) If L1 and L2 are nonregular, then LU L2 is nonregular. (d) If 1 and are nonregular, then LinL is nonregular. (e) If L1 is regular and is nonregular, then L,n L2 is nonregular. (f) If L1, c2,3, . . . are all regular, then Un,Ln is regular. (g) If L2 is regular and Ci is finite, then L1L2 is regular (h) If C1 UL2 is regular and L is finite, then L2 is regular. (i) If LiL2 is regular and L1 is finite, then L2 is regular