. (b) Find a regular expression for the language L defined recursively as follows:
1(a) Find a string which is not in the language represented
by .
(b) Find a regular expression for the language L defined recursively as follows:
Basis: 
Induction: If 
, then 
, 
, and 
.
Extremal: Nothing is in L unless it is obtained by the above clauses.
2. Recursively define the set U of all strings in {0,1} containing the substring 10.
3. Prove by induction on string y that 
.
4. Find a regular expression for the language of strings over the alphabet {a,b} which are accepted by the FA given by the following transition table.
The initial state is 
and the accepting states are and 
.