Relational Algebra Operations with Examples:

(i) Set Intersection: R ∩ S returns tuples present in both relations, requires union compatibility (same arity, domain). Example: Student ∩ CricketTeam gives students who are both enrolled and in cricket team. Can be expressed as R - (R - S).

(ii) Natural Join: Combines tuples from two relations where common attributes have equal values, automatically equating and projecting out duplicate column. Example: Student(sid, name) natural join Enroll(sid, cid) returns (sid, name, cid) where sid matches, without duplicate sid. Equivalent to cross product + selection + projection on equality of common attributes.

(iii) Division: R ÷ S returns values of attributes of R not in S that are associated with all values in S. Used for "for all" queries. Example: Completed(Student, Course) ÷ Required(Course) gives students who completed all required courses. If Completed has (Amit,DBMS),(Amit,OS) and Required has (DBMS),(OS), result is Amit.