SQL relational algebra - Division

How to understand division in relation
Definition ： Set up a relationship R Divide by relation S The result is relationship T, be T Include all in R But not in S Properties and their values in , And T Of Tuples And S All combinations of tuples of are in R in
 

 

There's a relationship R,S as well as RS, As shown in the figure , seek RS÷S Result
   

 

It is easy to get the result as ：{ Zhang San } 
    
    So you can easily see RS÷S The problem to be solved here is ：“ Get students who have taken all courses ”
   RS÷S Is that ：“ stay R and S The connection of RS in , Find out and S All tuples in are related R Tuples ”.

 R(X,Y)÷S(Y,Z) The operation of is in structured language SQL The statement can be expressed in the following form :

select distinct R.X from R as R1
where not exists
(
  select S.Y from S
   where not exists
   (
     select* from R as R2
     where R2.X = R1.X and R2.Y = S.Y
   )
);