Regular Expressions

Question

Can (ab* + b)* be written as (a + b)*.If so then how?

Answer 1

(ab*+b)* ---> put b* equal to null. Then it become (a+b)*.

Answer 2

For (ab* + b)*, the language it represents is (a, b, ab, ba, aa, ab, aab,.....)  i.e. all strings consisting of a and b.

And for (a + b)*, the language it represents is also (a, b, ab, ba, aa, ab, ...) i.e. again all strings consisting of a and b. Since both the regular expressions represent the same language, they are equivalent.