1. We can't trust all of them.
2. We trust none of them.
3. We can trust some of them.
4. We can trust not all of them.
Seriously, some grammar books (or blogs) say 1 is same with 2 while others say it is same with 3.
Which one really means sentence 1 between 2 and 3?
I also want to know if it is possible to say like sentence 4.
P.S. Grammar books I mention here are written by Korean authors of course.