Self-Doubt(P-NP class)

Question

$1)$ If the complement of NP-Complete problem is in NP, then can we also say , for this case complement of NP problem is in NP-Complete ?

$2)$ If the complement of NP-Complete problem is in Co-NP, then can we also say, for this case complement of Co-NP problem is in NP-Complete?

Comments

Can you make the sentences correct first? TOC is impossible if sentences are written like these.

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which sentence is incorrect?

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Both are not correct. "is it reverse true" is wrong usage.

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yes, I have corrected now. Check once plz if anything missing

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No. Still not correct. You can see similar sentences in previous year questions, standard books etc. and correct them. This English correction will surely get you more marks in GATE than decidability.

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Why still incorrect Sir? :(

I have written every words in it

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Yes, English is a language like Bengali. Just giving a collection of words won't make a proper sentence. They must be connected using correct connectives and in proper order.
You have used all the words required. But not in the correct way. I'm sure you can find same or similar question in standard books/online -- can you copy paste one.

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One question I found like this

$1)$ Prove the statement that if a language $L_{1}$ is $NP-complete$ and polynomial time reducible to $t_{2}$, then $L_{2}$ is also $NP-complete.$

Another one is

$2)$ $A$ is NP-hard iff $A'$ is $coNP-hard,$ where $A'$ does mean complement of $A.$
But both are not exactly accurate with this question

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Both are not "exactly same as the given ones".

I tried to edit the question -- but became confused with what exactly you meant. Are you talking about a specific language or language class? If it's the later what's the use of "if"?

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yes , not same.

Question came when I reading this answer https://gateoverflow.in/310347/there-rm-np%24-complete-language-%24l%24-whose-complement-np%24-then

language class means complexity class?

This question has some similarity I think https://cs.stackexchange.com/questions/80505/a-problem-is-np-hard-iff-its-complement-is-conp-complete

But unable to understand clearly

Is any easy way possible to understand it?

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The SE question is not valid -- the given answer is for a different claim if you see carefully. Anyway I suggest you to look at important things first -- which is English and able to write statements correctly even if not with 100% correct grammar. Then you can come back to TOC.

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@Arjun Sir

Chk this https://cs.stackexchange.com/questions/107401/complement-of-np-complete-can-be-in-np

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Yes, we need to get some editors here if people are not learning

https://cs.stackexchange.com/posts/107401/revisions

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@Arjun Sir

they compared NP and NP-Complete with a regular set and got answer.

Can NP and NP-Complete even be regular ? I never read this thing 

Such a easy solution for NP, NPC?

That even means we can compare NP, NPC with any CFL, CSL too?