Self Doubt

Question

Equal Or Not

$\Sigma ^{+} = L . L^{*} ?$

Comments

no bro its not you.. i know,

for the solution :

if we have to create a machine with symbols {a,b} than positive closure will be = {a,b,aa,bb,ab,ba....................... soon}

and if we are given a language which accepts aa only.. L={aa}

than L.L* will be (aa)+ which can never be equal to positive closure..

than why its wrong....?

.

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simply i got example

Sigma = {0,1}

L = {01}

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@arvin you are right 

Answer 1

If Σ={0,1}

 Σ+ = {0, 1, 00, 11, 01, 10, 000, 001,………..} : All combinations of 0 and 1 except ε(null string).

L is a language for given alphabet set (Σ). So, L can be anything (e.g. , L= {00, 11} then L.L*=L+ = all combination of 00 and 11)

There is no such relation between Σ+ and L.L*