I have quite a hard time understanding co-NP problems.
If we can reduce every problem to decision problem. NP problems should accept YES instances -> instances where the answer is yes. So for example for Traveling Salesman problem, we would ask "Is there a path that visits every city, and is shorter than N" ?
For co-NP problem, they should accept NO instance -> answer to them is NO. But given this, how would we formulate co-NP problem to Traveling Salesman problem I mentioned earlier? if we formulate it "Isn't there a path that visits every city and is shorter than N"? If there wasn't the path, the answer would be YES -> so it would be YES problem, if the answer was NO, we would have to try the path which would be same as YES problem.
So what is the difference? Was my co-NP decision problem to said TSP correct?
I have read wiki and tried to find some sources but nothing helped...
Thanks for help!