2 (a) a
(b) aa, ab, ba
(c) Add b in front of a string, and add a or b at the end of a string.
(d) Let L be the language to be defined.
Basis Clause:
Inductive Clause: For any
, xa, xb and bx are all in L.
Extremal Clause: Nothing is in L unless it is obtained from a finite number of
applications of the Basis and Inductive Clauses.
3. Basis Step: n = 0.
and
for any string x, it holds for n = 0.
Induction: Assume that
holds for an arbitrary n.
Then
by the definition of
by the property of REV.
by the induction hypothesis.
QED
4.