Mock Test

Question

Given Answer D) 

I think the answer should be A) 

Complement of L1 will be ( i = j or j = k) right so there can be a NPDA that will accept this right ?

Comments

just saying that complement of L1 is not what u showed

see this
$\text{complement of } \{{a^mb^n \mid m=n\}}=
\\ \text{complement of } \{{a^nb^n\}}=

\\ \overline{a^nb^n} = \{{a^mb^n \mid m\neq n\}} \cup \{{(a+b)^*ba(a+b)^*\}}$

here i have taken a small language, to show u complement.
When it comes to answer the type of language question, then we ignore union part. bcoz its always regular.

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so compliment is basically everything except the given language , so the compliment that I wrote is just a small part of the total compliment right ?

So will the compliment for the above question be -

( i = j or j = k) and all the strings that donot follow the order of the given language ( eg:bac, cba, etc...)

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^
exactly :)
but to answer questions in which they ask "Type of language" we can ignore

"all the strings that donot follow the order of the given language ( eg:bac, cba, etc...)"  

this part, bcoz this is always regular :)