regular expression

Question

the regular expression a*(ab*)* is same as

1.b*(ab*)*b*

2. a*+b*

3.(aba)*(a*+b)

4. none

Answer 1

Given regular expression a*(ab*)*

1.b*(ab*)*b* // generates babb or b* which is not possible by give regular expression

2. a*+b*  // same way 2. not able to generate ab

3.(aba)*(a*+b) // original expression can generate aaab but this can't .

So ans should be none.

Answer 2

2 Regular Expressions are same if they generate the same language... Here , a*(ab*)*  generates all the strings which start with 'a' But in options 1,2 and 3 , there is a possibility that string can be generate by b. So, answer will be (4) none