ME OTS 1

Question

I didn't get the solution. 

Comments

For example if L={$\epsilon$,a,b} then $L-{\epsilon}$ = {a,b}

but $L^+ $ = {{$\epsilon$},{a},{b},{a,b}} --> the $\epsilon$ here is as it in the language we placed the it but $L^*$ also  generates one $\epsilon$ which is removed in $L^+$.

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@Hemanth_13 

why we cant have that reasoning for sigma star ?

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Good question.. I think its because sigma is for input alphabet and our input alphabet will never contain $\epsilon$

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$\sum^*$ is one of the languages from $L$, and it doesn't imply statement $2$ to be TRUE for every case. Rest is explained by @Hemanth_13

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@Hemanth_13 

btw hemanth, when i looked closely your 1st comment,  you said 

$L^+$ = { $\epsilon$ ,..} 

but $L^+$ it self means one or more occurrence then how that language will have epsilon at the 1st place, i am confused here.