Re: NP problem and co-NP problem

On 13 Jul., 20:34, sanchopanch...@xxxxxx wrote:
On 13 Jul., 16:59, Zhu Guohun <ccgh...@xxxxxxxxxxxxxxxxxxxx> wrote:



On 7月13日, 下午10时20分, sanchopanch...@xxxxxx wrote:

Hello,

please let me post my last question again because the old name seems
to make problems with other threads.

Why is it true that NP = co-NP if there is an NP-complete language L
whose complement is in NP, too?

My textbook argues as follows (cL denotes the complement of L):
Because every NP language S is polynomial-time reducible to L, i.e.
S<L if follows that cS is polynomial-time reducible to cL, i.e.
cS<cL...
I don't understand this up to here. Why does cS<cL follow? Could
anybody help me?

Not correctly ( I don't know what is your textbook)
S<L can only follows cL < cS.

Yes, that is what I meant. Why does it follow?
Thanks,
S.

I am sorry for being so quick. This hasn't been what I meant.
My problem is to prove the two statements:
* Let L be NP-complete and L in co-NP then NP=co-NP
* Let L be NP-complete and cL in NP then NP=co-NP

Thanks,
Sancho
.