That one's not redundant; it says that illegal activities (in addition to violating the law) also violate the rules of the housing project. That kind of thing is bog-standard in all kinds of contracts, because including a clause like that makes your illegal activity grounds for terminating the contract. (In this case, the prohibition on illegal activities presumably allows the project to evict tenants who are convicted of crimes.)
Heh. This reminded me of http://itre.cis.upenn.edu/~myl/languagelog/archives/000012.h... .
"PERSONNEL WHO ARE NOT AUTHORIZED TO BE IN THE HANGAR ARE NOT AUTHORIZED TO BE IN THE HANGAR"