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Review of Definition of Regular Language
Definition of Set of Regular Languages :
Basis Clause: 
, {
}
and {a} for any symbol a 
are
regular languages.
Inductive Clause: If Lr and Ls
are regular languages, then
Lr 
Ls ,
LrLs
and Lr*
are regular languages.
Extremal Clause: Nothing is a regular language unless it is obtained from the above two clauses.
For example, let = {a, b}.
Then since {a} and {b} are regular languages, {a, b}
( = {a} {b} )
and {ab} ( = {a}{b} ) are regular languages. Also since {a} is regular, {a}*
is a regular language which is the set of strings consisting of a's such as
, a, aa, aaa, aaaa etc.
Note also that *, which is the set of strings
consisting of a's and b's, is a regular language
because {a, b} is regular.