Subset of a regular language

Question

Let L be a regular language over {a,b},   Suppose a new language defined as follows,

L = x1 , x2, x3, x4,........

L1 = x5, x10, x15 .....

L1 is defined as taking every string which is at positon 5, 10, 15 and so on, in other words, the positions that can be divided by 5.

Is L1 regular?

Comments

mam

this is relative to this  L=(a+b)*

      ==>{epsilon,a,b,aa,ab,ba,bb,aaa,aab,aba,abb,baa,bab,bba,bbb,aaaa,aaab,aaba,aabb

,abaa,abab,abba,abbb,baaa,baab,baba,babb,bbaa,bbab,bbba,bbbb..............}

 

Language is a SET of strings. Strings in language do not have a position

 

in the question

L = x1 , x2, x3, x4,........

L1 = x5, x10, x15

x5 ,x10 are relative to the  L

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@Gurdeep Saini

but how do u know a is starting string

I can take b as first string

then ba will be 5th one

and how do u know 1 length string comes before 2 length string?

Those all are assumption

So, b also can be 5th string

think about this

$\epsilon ,a,aa,ab,b$

I just go lexicographic and b is 5th one

So, u cannot assume correctly ,if the definition is not clear

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mam everything you are saying is correct but

in the question they given the generating  sequence of every string of the language

L = x1 , x2, x3, x4,........

L1 = x5, x10, x15 .....

and then they made a new language

but if they have given the set of string then  it may be regular or not

 

cunclusion: from the given  language i conclude the they given the generating sequence of  string of language

so  though the L1 is also regular

but if they have given the set of string then i am sure that L1 is not closed under the given operation