Decide whether each statement below is true or false. If it is true, prove it. If not, give a counterexample. The alphabet is {a, b}.

(a) If L1 L2 and L1 is not regular, then L2 is not regular.

(b) If L1 L2 and L2 is not regular, then L1 is not regular.

(c) If L1 and L2 are nonregular, then L1 L2 is nonregular. 1

(d) If L1 and L2 are nonregular, then L1 L2 is nonregular.

(e) If L1 is regular and L2 is nonregular, then L1 L2 is nonregular.

(f) If L1,L2,L3, . . . are all regular, then n=1Ln is regular.

(g) If L2 is regular and L1 is finite, then L1L2 is regular.

(h) If L1 L2 is regular and L1 is finite, then L2 is regular.

(i) If L1L2 is regular and L1 is finite, then L2 is regular