Yes, that's right translation, but there are only symmetrical relations in question - if first person knows or recognizes second person then second person recognizes first person as well.
EDIT - I just read again your post and realized you wrote about symmetric rule in last sentence. It's...
Hi
1. Homework Statement
On the party came n people. In the beginning all of them have had exactly 3 friends among party members. During party some people made new friends and at the end of the party everyone had exactly 4 friends among party members. Set all numbers n for which the following...