negative sentence form - they have many friends

Question

What the negative form of the offer - They have many friends. Will be?:

1. They have no friends.
2. They have not many friends.

which one is correct and why?

Answer 1

Your first example is very good.

The second is close, but 'have not many' is awkward and unusual. It would be better phrased as:

They do not have many friends.

"do not" is a frequently encountered idiom that will help you a lot.

https://www.englishoutsidethebox.com/2017/08/26/have-not-vs-do-not-have/

"have not" will be more commonly used when you are talking about something that you haven't done yet but could in the future:

I have not been late in a long time.

They have not had friends over this week.

I have not had breakfast. (but I may soon)

"Do not" is used to describe a present condition.

I do not have breakfast. (meaning right now)

Another way to rephrase your second example is:

They have not had many friends.

"do not have" and "have not had"

are both common patterns you should learn.

Answer 2

The first would be fine if there are zero friends, but that seems unduly limiting to me. The proper inverse of 'many' is usually 'few'. Granted, zero is indeed 'few', but there are other options as well. The second is closer but is poorly worded in my opinion.

So, I suggest:

They have few friends.

or

They do not have many friends. (preferably "They don't` have many friends" for this one)