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## Can I write a* + b* = (a + b)* ????

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NO  you cannot write
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To check equivalence of two regex create minimal DFA for both regex and if they are same then yes they are equivalent.
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sumit goyal 1 please explain the difference

+1
a* + b *  wil give { a , aa ,aaa ,aaaa ,......  , b,bb,bbb,bbbb,bbbb  , epsilon }

(a+b)* will give all possible combinations
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so how to create a DFA for this? a* + b *
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It is drawn like this

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sumit goyal 1 You forgot dead state.$4$ states will be there moreover first state is final

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i cretaed a nfa , so i didnot take dead state ,

+1 vote

$1^{st}$ one is RHS.
$2^{nd}$ one is LHS.
LHS $\neq$ RHS

No ,because both are not same as u can see by the 1st REstring produce like ab,aabb.a,b,aa,bbetc but u can't get string like aba,aaabbabab,ababa etc .

whereas by the 2nt RE u will get all string produce by a and b.