Consider the following statements regarding alphabet and language inequalities-S1- - -S2-L-L-Which of the above statements are always true-

Only nbsp;S_1 holds true. The problem in nbsp;S_2 is that, if nbsp;"ϵ " belongs to L. RHS will contain nbsp;ϵ, but LHS won't, so the equality will not h ...

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Standard XII

Mathematics

Modulus of a Complex Number

Consider the ...

Question

Consider the following statements regarding alphabet and language inequalities:
$S_{1} : \sum^{} - {ϵ} = \sum^{+}$

$S_{2} : L^{} - {ϵ} = L^{*}$
Which of the above statements are always true?

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Solution

Only $S_{1}$ holds true. The problem in $S_{2}$ is that, if $" ϵ "$ belongs to L. RHS will contain $ϵ$ , but LHS won't, so the equality will not hold. Therefore $S_{2}$ will be false.

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Consider the following statements regarding alphabet and language inequalities: S1:∑∗−{ϵ}=∑+ S2:L∗−{ϵ}=L∗ Which of the above statements are always true?

Only S1 holds true. The problem in S2 is that, if "ϵ" belongs to L. RHS will contain ϵ, but LHS won't, so the equality will not hold. Therefore S2 will be false.

Consider the following statements regarding alphabet and language inequalities:
$S_{1} : \sum^{} - {ϵ} = \sum^{+}$

$S_{2} : L^{} - {ϵ} = L^{*}$
Which of the above statements are always true?

Only $S_{1}$ holds true. The problem in $S_{2}$ is that, if $" ϵ "$ belongs to L. RHS will contain $ϵ$ , but LHS won't, so the equality will not hold. Therefore $S_{2}$ will be false.