# Converting sets into regular expressions

In my book:

• The set {abb, a, b, bba} is said to be converted into regular expression abb + a + b + bba.
• The set {01, 10} to regular expression 01 + 10

Does the +'s here represent concatenation or union?

• In regular expressions, $+$ is union – vonbrand Nov 12 '15 at 9:37
• There is only one true answer: looks at the definition. – Raphael Nov 12 '15 at 10:59

We don't quite convert a set to a regular expression. Rather, we give a regular expression for a language (i.e., a regular expression which defines the same language). For example, a regular expression for the language $\{01,10\}$ is $01+10$, and a regular expression for the language $\{abb,a,b,bba\}$ is $a+b+abb+bba$. There can be other regular expressions. For example, another regular expression for the second language is $a(\epsilon+bb) + b(\epsilon+ba)$.