Proof can be understood by considering an example-
- Let A be Regular Language denoting A=
0*.
- Let B be Regular Language denoting
B= 1*.
- Then concatenation of A,B is given as
AB.
- Mathematically, AB will represent the following
language-
AB = 0*1*
- Now, analyzing the Right Hand Side of the above expression-
i.e; 0*1*. 0*1* is a language which represents the strings in which
set of zero or more number of zeros is followed by a set of zero or
more number of ones.
- Strings like {' ', '01' , '001', '011', '0011', .......}
- Right Hand Side also contains the quantifier *. ' * ' is only
used in Regular Languages.
- When a Language can be defined to represent the collection of
strings then the language is obvious to be called as Regular
Expressions.
With considering the above few points, AB is proved to be
regular.