MadeEasy Test Series: Theory Of Computation - Regular Expressions

Question

$\Sigma ^{*} - {\left \{ \epsilon \right \}} = \Sigma ^{+} $

$L^{*} - {\left \{ \epsilon \right \}} = L^{+}$

Which of the above is always true ?

Comments

Should be A, I guess. In B, if $L = {\phi}$, I don't think it holds.

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2nd inequality is false also for $L = \left \{ \epsilon \right \}$

RIght ??

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Yes, it is false for that too.

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@goxul how it is not holding for L= phi

if L=phi

then L*=epsilon

L* - {epsilon} is again phi..isin't?

Answer 1

The second one holds true, only If ϵ doesn't belong to L. If a language contains ϵ, then the RHS will always contain ϵ, and LHS won't. Hence second one is false.

Comments

no ,how can it be?

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@jatin khachane 1   Invalid.

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Thanks and sorry for such silly doubt