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$L^{*}-\{{\epsilon }\}=L^{+}$. True or False? (Given L is a language)

in Theory of Computation by (93 points)
edited by | 88 views
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but here it not a string it's language right ??

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L is not alphabets, it is a language. is it true for language also?
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false
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False for $L=\left \{ \right \}$
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yes got it. Thanks for testcase
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If it was like:

L* -{ ϵ } = L+

given L is a language made from (a,b) then?

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When we got a contradicting case why check other, the statement is false
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How? can you please explain? @Shobhit Joshi

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$L=\left\{\right \}$, for this the given statement is not True. Hence, the statement is False
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I am asking it in general :

IF this is given in exam then what will be our approach 

If it was like:

L* -{ ϵ } = L+

given L is a language made from (a,b) then?

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Even if L is empty, it's Kleene closure will have epsilon.
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Can someone confirm it

 

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