Regular expression

Question

Is a*b* + b*a* = ( a + b)*       ______

Comments

No. a*b* is all strings that have a's followed by b's. b*a* is all strings that have b's followed by a's. However, in (a+b)*, you can have any sequence of a's and b's. Eg abbababa

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In general for such questions, you can try finding strings in one which are not present in the other.

In this example, the RHS generates "abab" which is not generated by the LHS. Hence, they are not equivalent.

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No (a+b)*=(a*+b*)*=(a*b*)*=(a*+b) *=(a+b*)*=a*(ba) *=b*(ab)*

Hence these are the possibilities and certainly the given expression is wrong

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How is (a+b)* = a*(ba)* ? How a*(ba)* generates bbb?

Answer 1

a*b*= a,b,ab,aab aabb,aabbbb.....

b*a*= a,b,ab,ba,bba,bbaaa........

So we can genrate only string like a followed b or b followed a.

But we can not genrate syring  like aba,bab,aaba,.....

So its not equal to (a+b)*

Answer 2

No, both LHS !=RHS becoz in a*b* we have a followed by b i.e epsilon,a,b,ab,aa, bb,aabb,abb,aab,abbb

in b*a* we have b followed a i.e epsilon,b,a,bb,aa,bbaa,baa,bba,bbbaaa etc

(a+b)*= (a*b*)*, (a*+b)*,(a+b*)* any sequence of a and b are acceptable