Find a 3NF decomposition of the following relation scheme: University (Faculty, Dean, Department, Chair, Professor, Rank, Student}. The University relation satisfies the following set of functional dependencies:

{Faculty → Dean, Dean → Faculty, Department → Chair, Professor →Rank Chair, Department → Faculty, Student → DepartmentFacultyDean,

ProfessorRank → DepartmentFaculty}

Is the decomposition non-loss and dependency preserving?