Basic doubt

Question

If $L = \{a^nb^n : n\geq 0\}$
then, $L^2=?$

Comments

I'm studying from Peterlinz book it is given $L^2$={$a^n$$b^n$$a^m$$b^m$ :n>=0 , m>=0}
Can anyone explain this?

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@Arjun sir @Shaik Masthan sir

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aimhigh

According to you what should be the answer ??

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L = { a$^n.b^n$ | n ≥ 0 } ===> L = {∈,ab,aabb,aaabbb,aaaabbbb,.....}

L$^2$ = $\color{red}{L} . \color{green}{L} = \color{red}{\{∈,ab,aabb,aaabbb,aaaabbbb,.....\}} . \color{green}{\{∈,ab,aabb,aaabbb,aaaabbbb,.....\}}$

that means, concatenate each string in $\color{red}{L}$  with each string of $\color{green}{L}$

L$^2 = \{\underbrace{\color{green}{∈,ab,aabb,aaabbb,aaaabbbb,.....}}\;\;,\underbrace{\color{red}{ab},\color{red}{ab}\color{green}{ab},\color{red}{ab}\color{green}{aabb},\color{red}{ab}\color{green}{aaabbb},\color{red}{ab}\color{green}{aaaabbbb},.....}\;\;,\underbrace{\color{red}{aabb},\color{red}{aabb}\color{green}{ab},\color{red}{aabb}\color{green}{aabb},\color{red}{aabb}\color{green}{aaabbb},\color{red}{aabb}\color{green}{aaaabbbb},.....}$

$\;\;,\underbrace{\color{red}{aaabbb},\color{red}{aaabbb}\color{green}{ab},\color{red}{aaabbb}\color{green}{aabb},\color{red}{aaabbb}\color{green}{aaabbb},\color{red}{aaabbb}\color{green}{aaaabbbb,.....}}\;\;,\}$

 

Now can you conclude the pattern ?

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@aimhigh

tag the names correctly, otherwise we didn't get notify !

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Thank you so much Shaik sir.. I got explanation.

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How you all are tagging to other users I have also written correct names but it is just plain text

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to tag someone, first type @, then type name

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@Shaik Masthan

Answer 1

$L^2 =L.L =a^nb^na^mb^m |n,m>=0$