regular exp[ression

Question

Which of the following regular expression identities are true ?

(A) (r + s)* = r* s*

(B) (r + s)* = r* + s*

(C) (r + s)* = (r*s*)*

(D) r* s* = r* + s*

Comments

D should be answer bcz c option 's lhs also generate sr which rhs is incapable to generate

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question is which one is correct

Answer 1

(r + s)* = (r*s*)*

Comments

need explaination.....

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Try generating strings from both sides

RHS is capable of producing strings like LHS in  option 3 only

in first  rsr is not generated by RHS

In second RHS only produces rrrr.... or ssss..... which is not like LHS

In fourth option RHS only creates rrrr.... or sssss unlike LHS (rrrrr...sssss...)

Answer 2

c) (r+s)*=(r*s*)*

Comments

Can you please explain it?

Answer 3

Both b and c

Comments

not c

Answer 4

(r + s)* = (r* + s*)* = (r*s*)*=(r* + s)*=(r+s*)*=a*(ba*)*=b*(ab*)*

Therfore option C will be right option for it.

Comments

(r+s*)*=a*(ba*)*=b*(ab*)* 

is it right