Textbook pp. 194 - 195:
5.20 (a) To distinguish and , , append .
Then but .
5.26 (a) No. Let and .
(c) No. Let and .
Then is regular but neither nor is regular.
(g) Yes. Since L1 L2
is regular, L1 - L2 =
L1 - ( L1 L2)
is regular. Now L2 = ( L1
L2 ) - ( L1 L2 ). Hence if
L1
L2 is regular, L2 is regular, since
the difference of regular languages is regular.
5.27 (c) Let be the infinite set. Then and
for can be distinguished with respect to the language in question by appending
to them (0 is in the middle for but not for ). Therefore the language is not regular.