Define the Division Operation of Relational Algebra

Let R be a relation comprising attributes (A1,...Ap,Ap+1,...An) and S comprising attributes (Ap+1,...An) 

DEF: Division

The division of R by S, represented R ÷ S, provides a new relation Q, the quotient of the division, like Q has attributes (A1...Ap) and every tuple of Q must take place in R in combination along with every  tuple in S. 

The division can be acquired from the difference, the Cartesian product and the projection like this:

 R ÷ S = T - Y, where T = π_A1,...Ap (R ) and Y =  π_A1,...Ap ( (T X S) - R)