Textbook pp. 76 - 79:
2.59 (c) Induction on n.
Basis: n = 0. . . Hence .
Also .
Hence it holds for n = 0.
Induction: Assume for an arbitrary k.
because (xy)r = yrxr.
2.39 (b) L is the set of strings having exactly one a and any number of bs before and after a.
2.40 (d) Basis:
Induction: If , then , , , and .
Extremal: Nothing is in U unless it is obtained by the Basis and Induction.
(f) Basis:
Induction: If , then and .
Extremal: Nothing is in W unless it is obtained by the Basis and Induction.