To understand the answer it is necessary that you understand the meaning of division operation – “Division operation A/B is defined as the set of all x values (in the form of unary tuples) such that for every y value in (a tuple of) B, there is a tuple (x, y) in A”
lets think meaning of everything lets B is relation with different values of Y here let assume here Y = (1,2,3)
and Relation A have tuples in which x is paired with different values of Y – some x are paired with some value of y and some are paired with every value of Y. example A = {(a,1)(b,1)(b,2)(c,1)(c,2)(c,3)} here you can see that C is paired with all value of Y then answer of A/B will be c
now how to obtain this result with basic operations..
clearly, I know that i have to remove the tuples with only some values of Y but unfortunately i cant remove them directly
but we can remove the tuples which are paired up every value of B(Y) how?
first we π_x (A) × B which will give us the tuples {(a,1)(a,2)(a,3)(b,1)(b,2)(b,3)(c,1)(c,2)(c,3)} so if I substract A from this c will be completely delete from π_x (A) × B and we are left with tuples of a and b which we dont want so
we substract them from our A which will give out our answer that is c
hope it will help some