I want to know the negation of the following sentence.
"$x$ and $y$ have chatted over the Internet".
I thought the negation of this is that "$x$ and $y$ have not chatted over the Internet" and understood that $x,y$ have not chatted each other and It doesn't mean $x$ and $y$ have not chatted in their lifetime.
Am I right? Sorry for poor English.
Yes, the negation is "$x$ and $y$ have not chatted over the Internet".
I'm not sure what you're getting at with "It doesn't mean $x$ and $y$ have not chatted in their life time". The sentence says nothing about whether they have chatted in any other way than over the Internet (e.g. in person).